]>
2017
10
1
ISSN 2008-1898
336
A study on the differential and sub-differential of fuzzy mapping and its application problem
A study on the differential and sub-differential of fuzzy mapping and its application problem
en
en
In this paper, firstly, we gain some basic properties and characterization theorems of the differential and local sub-differential
of the fuzzy mapping, obtain an important result that the local sub-differential of fuzzy mapping is an empty set or a convex
set. Secondly, we generalize the concept of local differentiability of fuzzy mapping, and obtain some basic properties about
the concept. At last, we study the relationships between sub-differential of fuzzy mapping and differential of convex fuzzy
mappings. Moreover, a sufficient condition that a class of fuzzy mapping have convex extension is gained.
1
17
Yu-E
Bao
College of Mathematics
Inner Mongolia University for Nationalities
China
byebed@163.com
Jin-Jun
Li
College of Mathematics
Inner Mongolia University for Nationalities
China
Fuzzy number
fuzzy mapping
differential (sub-differential)
convexification fuzzy mapping
convex extension.
Article.1.pdf
[
[1]
E. Ammar, J. Metz, On fuzzy convexity and parametric fuzzy optimization, Fuzzy Sets and Systems, 49 (1992), 135-141
##[2]
Y. E. Bao, C.-X. Wu, Convexity and strict convexity of fuzzy mappings, (Chinese) J. Harbin Inst. Tech., 39 (2007), 639-641
##[3]
Y. E. Bao, C.-X. Wu, Semistrictly convex fuzzy mappings, J. Math. Res. Exposition, 30 (2010), 571-580
##[4]
B. Bede, S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 (2005), 581-599
##[5]
B. Bede, L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 230 (2013), 119-141
##[6]
S. S. L. Chang, L. A. Zadeh, On fuzzy mapping and control, IEEE Trans. Systems, Man, and Cybernet., SMC-, 2 (1972), 30-34
##[7]
D. Dubois, H. Prade, Towards fuzzy differential calculus, I, II, III, Fuzzy Sets and Systems, 8 (1982), 1-17
##[8]
Z. T. Gong, H. X. Li , Derivatives and gradients of fuzzy mappings and their applications, (Chinese) Appl. Math. J. Chinese Univ. Ser. A, 25 (2010), 229-238
##[9]
S. Nanda, K. Kar , Convex fuzzy mappings, Fuzzy Sets and Systems, 48 (1992), 129-132
##[10]
M. Panigrahi, G. Panda, S. Nanda , Convex fuzzy mapping with differentiability and its application in fuzzy optimization, European J. Oper. Res., 185 (2008), 47-62
##[11]
M. L. Puri, D. A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl., 91 (1983), 552-558
##[12]
R. T. Rockafellar , Convex analysis, Princeton Mathematical Series, Princeton University Press, Princeton, N.J. (1970)
##[13]
Y.-R. Syau, Differentiability and convexity of fuzzy mappings, Comput. Math. Appl., 41 (2001), 73-81
##[14]
G.-X. Wang, C.-X. Wu, Directional derivatives and subdifferential of convex fuzzy mappings and application in convex fuzzy programming, Fuzzy Sets and Systems, 138 (2003), 559-591
##[15]
C. X. Wu, C. Wu, The supremum and infimum of the [a] set of fuzzy numbers and its [their] application, J. Math. Anal. Appl., 210 (1997), 499-511
##[16]
C. Zhang, X.-H. Yuan, E. S. Lee, Duality theory in fuzzy mathematical programming problems with fuzzy coefficients, Comput. Math. Appl., 49 (2005), 1709-1730
##[17]
C. Zhang, X.-H. Yuan, E. S. Lee, Convex fuzzy mapping and operations of convex fuzzy mappings, Comput. Math. Appl., 51 (2006), 143-152
]
Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones
Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones
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en
We introduce the concept of order-Ćirić-Lipschitz mappings, and prove some fixed point theorems for such kind of mappings
in normed vector spaces without assuming the normalities of cones by using upper and lower solutions method, which
improve many existing results of order-Lipschitz mappings in Banach spaces or Banach algebras. It is worth mentioning that
even in the setting of normal cones, the main results in this paper are still new since the sum of spectral radius or the sum of
restricted constants may be greater than or equal to 1.
18
26
Zhilong
Li
School of Statistics
Research Center of Applied Statistics
Jiangxi University of Finance and Economics
Jiangxi University of Finance and Economics
China
China
lzl771218@sina.com
Shujun
Jiang
Department of Mathematics
Jiangxi University of Finance and Economics
China
jiangshujuns@sina.com
Fixed point
order-C´ iric´-Lipschitz mapping
Picard-complete
w-complete.
Article.2.pdf
[
[1]
S. Banach , Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundam. Math., 3 (1922), 133-181
##[2]
S. K. Chatterjea , Fixed point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727-730
##[3]
L. B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math., 12 (1971), 19-26
##[4]
K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin (1985)
##[5]
S. Jiang, Z. Li, Extensions of Banach contraction principle to partial cone metric spaces over a non-normal solid cone, Fixed Point Theory Appl., 2013 (2013 ), 1-9
##[6]
6] S. Jiang, Z. Li, Fixed point theorems of order-Lipschitz mappings in Banach algebras, Fixed Point Theory Appl., 2016 (2016 ), 1-10
##[7]
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76
##[8]
M. A. Krasnosel’skiĭ, P. P. Zabreĭko, Geometrical methods of nonlinear analysis, Springer-Verlag, Berlin (1984)
##[9]
Z. Li, S. Jiang, Common fixed point theorems of contractions in partial cone metric spaces over nonnormal cones, Abstr. Appl. Anal., 2014 (2014 ), 1-8
##[10]
J.-X. Sun, Iterative solutions of nonlinear operator, (Chinese) J. Engin. Math., 6 (1989), 12-17
##[11]
X. Y. Zhang, J. X. Sun, Existence and uniqueness of solutions for a class of nonlinear operator equations and its applications, (Chinese) Acta Math. Scientia, 25 (2005), 846-851
]
On order-Lipschitz mappings in Banach spaces without normalities of involving cones
On order-Lipschitz mappings in Banach spaces without normalities of involving cones
en
en
We prove a new fixed point theorem of order-Lipschitz mappings in Banach spaces without assumption of normalities of the
involving cones, which presents a positive answer to a problem raised in [S. Jiang, Z. Li, Fixed Point Theory Appl., 2016 (2016),
10 pages] and improves the corresponding results of Krasnoselskii and Zabreiko’s and Zhang and Sun’s since the normality of
the involving cone is removed.
27
33
Zhilong
Li
School of Statistics
Research Center of Applied Statistics
Jiangxi University of Finance and Economics
Jiangxi University of Finance and Economics
China
China
lzl771218@sina.com
Shujun
Jiang
Department of Mathematics
Jiangxi University of Finance and Economics
China
jiangshujuns@sina.com
Rade
Lazovic
Faculty of Organizational Sciences
University of Belgrade
Serbia
lazovic@fon.bg.ac.rs
Fixed point theorem
order-Lipschitz mapping
Picard-completeness
non-normal cone.
Article.3.pdf
[
[1]
K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin (1985)
##[2]
S. Jiang, Z. Li, Extensions of Banach contraction principle to partial cone metric spaces over a non-normal solid cone, Fixed Point Theory Appl., 2013 (2013 ), 1-9
##[3]
S. Jiang, Z. Li, Fixed point theorems of order-Lipschitz mappings in Banach algebras, Fixed Point Theory Appl., 2016 (2016 ), 1-10
##[4]
M. A. Krasnosel’skiĭ, P. P. Zabreĭko, Geometrical methods of nonlinear analysis, Springer-Verlag, Berlin (1984)
##[5]
Z. Li, S. Jiang, Common fixed point theorems of contractions in partial cone metric spaces over nonnormal cones, Abstr. Appl. Anal., 2014 (2014 ), 1-8
##[6]
J.-X. Sun, Iterative solutions of nonlinear operator, (Chinese) J. Engin. Math., 6 (1989), 12-17
##[7]
X. Y. Zhang, J. X. Sun, Existence and uniqueness of solutions for a class of nonlinear operator equations and its applications, (Chinese) Acta Math. Scientia, 25 (2005), 846-851
]
Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces
Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces
en
en
The present paper studies almost fixed point property for digital spaces whose structures are induced by Marcus-Wyse
(M-, for brevity) topology. In this paper we mainly deal with spaces \(X\) which are connected M-topological spaces with M-adjacency
(MA-spaces or M-topological graphs for short) whose cardinalities are greater than 1. Let MAC be a category whose objects,
denoted by Ob(MAC), are MA-spaces and morphisms are MA-maps between MA-spaces (for more details, see Section 3), and
MTC a category of M-topological spaces as Ob(MTC) and M-continuous maps as morphisms of MTC (for more details, see
Section 3). We prove that whereas any MA-space does not have the fixed point property (FPP for short) for any MA-maps, a
bounded simple MA-path has the almost fixed point property (AFPP for short). Finally, we refer the topological invariant of the
FPP for M-topological spaces from the viewpoint of MTC.
34
47
Sang-Eon
Han
Department of Mathematics Education, Institute of Pure and Applied Mathematics
Chonbuk National University, 54896
Republic of Korea
sehan@jbnu.ac.kr
Digital topology
fixed point property
Marcus-Wyse topology
MA-map
MA-isomorphism
MA-homotopy
MA-space
MA-contractibility
M-topological graph
almost fixed point property.
Article.4.pdf
[
[1]
P. Alexandroff, Diskrete Räume, Mat. Sb., 2 (1937), 501-518
##[2]
L. Boxer , A classical construction for the digital fundamental group, J. Math. Imaging Vision, 10 (1999), 51-62
##[3]
R. F. Brown, The Lefschetz fixed point theorem, Scott, Foresman and Co., , Glenview, Ill.-London (1971)
##[4]
V. A. Chatyrko, S.-E. Han, Y. Hattori, Some remarks concerning semi-\(T_{1/2}\) spaces , Filomat, 28 (2014), 21-25
##[5]
O. Ege, I. Karaca, Lefschetz fixed point theorem for digital images, Fixed Point Theorey Appl., 2013 (2013 ), 1-13
##[6]
S.-E. Han, On the classication of the digital images up to a digital homotopy equivalence, J. Comput. Commun. Res., 10 (2000), 194-207
##[7]
S.-E. Han, Non-product property of the digital fundamental group, Inform. Sci., 171 (2005), 73-91
##[8]
S.-E. Han, On the simplicial complex stemmed from a digital graph, Honam Math. J., 27 (2005), 115-129
##[9]
S.-E. Han, Equivalent \((k_0, k_1)\)-covering and generalized digital lifting, Inform. Sci., 178 (2008), 550-561
##[10]
S.-E. Han, The k-homotopic thinning and a torus-like digital image in \(Z^n\), J. Math. Imaging Vision, 31 (2008), 1-16
##[11]
S.-E. Han, KD-\((k_0, k_1)\)-homotopy equivalence and its applications, J. Korean Math. Soc., 47 (2010), 1031-1054
##[12]
S.-E. Han, Fixed point theorems for digital images, Honam Math. J., 37 (2015), 595-608
##[13]
S.-E. Han, Generalizations of continuity of maps and homeomorphisms for studying 2D digital topological spaces and their applications, Topology Appl., 196 (2015), 468-482
##[14]
S.-E. Han, Banach fixed point theorem from the viewpoint of digital topology, J. Nonlinear Sci. Appl., 9 (2016), 895-905
##[15]
S.-E. Han, Contractibility and fixed point property: the case of Khalimsky topological spaces, Fixed Point Theory Appl., 2016 (2016 ), 1-20
##[16]
S.-E. Han, W.-J. Chun, Classification of spaces in terms of both a digitization and a Marcus Wyse topological structure, Honam Math. J., 33 (2011), 575-589
##[17]
S.-E. Han, B. G. Park, Digital graph \((k_0, k_1)\)-homotopy equivalence and its applications, http://atlas-conferences. com/c/a/k/b/35.htm, (2003)
##[18]
S.-E. Han, B. G. Park, Digital graph \((k_0, k_1)\)-isomorphism and its applications, http://atlas-conferences.com/c/a/ k/b/36.htm, (2003)
##[19]
S.-E. Han, W. Yao, Homotopy based on Marcus-Wyse topology and its applications, Topology Appl., 201 (2016), 358-371
##[20]
G. T. Herman, Oriented surfaces in digital spaces, CVGIP: Graph. Models Image Proc., 55 (1993), 381-396
##[21]
E. Khalimsky , Motion, deformation and homotopy in finite spaces, Man and CyberneticsProceedings of the IEEE International Conference on Systems, , (1987), 227-234
##[22]
E. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl., 36 (1990), 1-17
##[23]
T. Y. Kong, A. Rosenfeld, Topological algorithms for digital image processing, Elsevier Science, Amsterdam (1996)
##[24]
S. Lefschetz, Topology , Amer. Math. Soc. , (1930), -
##[25]
S. Lefschetz , On the fixed point formula, Ann. of Math., 38 (1937), 819-822
##[26]
A. Rosenfeld , Digital topology, Amer. Math. Monthly, 86 (1979), 621-630
##[27]
A. Rosenfeld, Continuous functions on digital pictures, Pattern Recogn. Lett., 4 (1986), 177-184
##[28]
J. Šlapal, Topological structuring of the digital plane, Discrete Math. Theor. Comput. Sci., 15 (2013), 165-176
##[29]
F. Wyse, D. Marcus, Solution to problem 5712, Amer. Math. Monthly, 77 (1970), 1-1119
]
On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class
On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class
en
en
We prove that the invariant probability measure of an orientation preserving circle homeomorphism f with several break
points (at which the derivative \(\acute{f}\) has jumps) is singular with respect to Lebesgue measure, if \(\acute{f}\) satisfies certain condition and
the product of jump ratios at break points is non-trivial.
48
59
Sokhobiddin
Akhatkulov
School of Mathematical Sciences, Faculty of Science and Technology
University Kebangsaan Malaysia
Malaysia
akhatkulov@yahoo.com
Mohd. Salmi Md.
Noorani
School of Mathematical Sciences, Faculty of Science and Technology
University Kebangsaan Malaysia
Malaysia
msn@ukm.edu.my
Habibulla
Akhadkulov
School of Quantitative Sciences
University Utara Malaysia
Malaysia
akhadkulov@yahoo.com
Break point
circle homeomorphism
invariant measure
rotation number.
Article.5.pdf
[
[1]
Kh. A. Akhadkulov, On some circle homeomorphisms with break-type singularities, (Russian) Uspekhi Mat. Nauk, 61 (2006), 183–184, translation in Russian Math. Surveys, 61 (2006), 981-983
##[2]
H. Akhadkulov, M. S. M. Noorani, S. Akhatkulov, Renormalizations of circle diffeomorphisms with a break-type singularity, ArXiv, 2015 (2015 ), 1-26
##[3]
V. I. Arnol’d , Small denominators, I , (Russian) Izv. Akad. Nauk SSSR Ser. Mat.Mapping the circle onto itself, , 25 (1961), 21-68
##[4]
I. P. Cornfeld, S. V. Fomin, Ya. G. Sinaı, Ergodic theory, Translated from the Russian by A. B. Sosinskiı, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, New York (1982)
##[5]
W. de Melo, S. van Strien, One-dimensional dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Springer-Verlag, Berlin (1993)
##[6]
A. Denjoy, Sur les courbes définies par les équations différentielles a la surface du tore, J. Math. Pure Appl., 11 (1932), 333-376
##[7]
A. A. Dzhalilov, K. M. Khanin , On an invariant measure for homeomorphisms of a circle with a point of break, Funct. Anal. Appl., 32 (1998), 153-161
##[8]
A. Dzhalilov, I. Liousse, D. Mayer, Singular measures of piecewise smooth circle homeomorphisms with two break points, Discrete Contin. Dyn. Syst., 24 (2009), 381-403
##[9]
A. A. Dzhalilov, D. Maıer, U. A. Safarov, Piecewise-smooth circle homeomorphisms with several break points, (Russian) Izv. Ross. Akad. Nauk Ser. Mat., 76 (2012), 101–120, translation in Izv. Math., 76 (2012), 94-112
##[10]
M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle a des rotations, (French) Inst. Hautes tudes Sci. Publ. Math., 49 (1979), 5-233
##[11]
J. Hu, D. P. Sullivan, Topological conjugacy of circle diffeomorphisms, Ergodic Theory Dynam. Systems, 17 (1997), 173-186
##[12]
Y. Katznelson, D. Ornstein, The absolute continuity of the conjugation of certain diffeomorphisms of the circle, Ergodic Theory Dynam. Systems, 9 (1989), 681-690
##[13]
J. Moser , A rapidly convergent iteration method and non-linear differential equations, II, Ann. Scuola Norm. Sup. Pisa, 20 (1966), 499-535
##[14]
Ya. G. Sinaı, K. M. Khanin, Smoothness of conjugacies of diffeomorphisms of the circle with rotations, (Russian) Uspekhi Mat. Nauk, 44 (1989), 57–82, translation in Russian Math. Surveys, 44 (1989), 69-99
##[15]
E. B. Vul, K. M. Khanin, Homeomorphisms of the circle with fracture-type singularities, (Russian) Uspekhi Mat. Nauk, 45 (1990), 189–190, translation in Russian Math. Surveys, 45 (1990), 229-230
##[16]
J. C. Yoccoz, Il n’y a pas de contre-exemple de Denjoy analytique, (French) [There are no analytic Denjoy counterexamples] C. R. Acad. Sci. Paris Sér. I Math., 298 (1984), 141-144
##[17]
A. Zygmund, Trigonometric series, Vol. I, II, Third edition, With a foreword by Robert A. Fefferman,/ Cambridge Mathematical Library, Cambridge University Press, Cambridge (2002)
]
On a singular time-fractional order wave equation with Bessel operator and Caputo derivative
On a singular time-fractional order wave equation with Bessel operator and Caputo derivative
en
en
This paper deals with the study of the well-posedness of a mixed fractional problem for the wave equation defined in a
bounded space domain. The fractional time derivative is described in the Caputo sense. We prove the existence and uniqueness
of solution as well as its dependence on the given data. Our results develop and show the efficiency and effectiveness of the
functional analysis method when we deal with fractional partial differential equations instead of the nonfractional equations
which have been extensively studied by many authors during the last three decades.
60
70
Said
Mesloub
Mathematics Department, College of Science
King Saud University
Saudi Arabia
mesloub@ksu.edu.sa
Imed
Bachar
Mathematics Department, College of Science
King Saud University
Saudi Arabia
abachar@ksu.edu.sa
Caputo derivative
solvability of the problem
fractional differential equation
initial boundary value problem.
Article.6.pdf
[
[1]
G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135 (1988), 501-544
##[2]
G. Adomian, Solving frontier problems of physics: the decomposition method, With a preface by Yves Cherruault, Fundamental Theories of Physics, Kluwer Academic Publishers Group, Dordrecht (1994)
##[3]
A. A. Alikhanov, A priori estimates for solutions of boundary value problems for fractional-order equations, Dier. Equ., 46 (2010), 660-666
##[4]
L. Debnath, D. D. Bhatta, Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics, Fract. Calc. Appl. Anal., 7 (2004), 21-36
##[5]
A. M. A. El-Sayed, M. Gaber, The Adomian decomposition method for solving partial differential equations of fractal order in finite domains, Phys. Lett. A, 359 (2006), 175-182
##[6]
N. Engheta, On fractional calculus and fractional multipoles in electromagnetism, IEEE Trans. Antennas and Propagation, 44 (1996), 554-566
##[7]
A. Freed, K. Diethelm, Y. Luchko , Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus: First annual Report, NASA Technical Reports Server (NTRS), United States (2002)
##[8]
R. Gorenfo , Abel integral equations with special emphasis on applications, Lectures in Mathematical Sciences, The University of Tokyo, Graduate School of Mathematical Sciences (1996)
##[9]
J. H. He, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol., 15 (1999), 86-90
##[10]
R. Hilfer (Ed.), Applications of fractional calculus in physics, World Scientific Publishing Co., Inc., River Edge, NJ (2000)
##[11]
H. Jafari, V. Daftardar-Gejji, Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition, Appl. Math. Comput., 180 (2006), 488-497
##[12]
T. Kaplan, L. J. Gray, S. H. Liu, Self-affine fractal model for a metal-electrolyte interface, Phys. Rev. B, 35 (1987), 5379-5381
##[13]
A. M. Keighttey, J. C. Myland, K. B. Oldham, P. G. Symons, Reversible cyclic voltammetry in the presence of product, J. Electroanal. Chem., 322 (1992), 25-54
##[14]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[15]
O. A. Ladyzhenskaya, The boundary value problems of mathematical physics, Springer-VerlagTranslated from the Russian by Jack Lohwater [Arthur J. Lohwater], Applied Mathematical Sciences, , New York (1985)
##[16]
A. Le Mehaute, G. Crepy, Introduction to transfer and motion in fractal media: the geometry of kinetics, Solid State Ion., 9 (1983), 17-30
##[17]
F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fractals, 7 (1996), 1461-1477
##[18]
F. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics, Fractals and fractional calculus in continuum mechanics, Udine, (1996), 291–348, CISM Courses and Lectures, Springer, Vienna (1997)
##[19]
F. Mainardi, Fractional calculus and waves in linear viscoelasticity, An introduction to mathematical models. Imperial College Press, London (2010)
##[20]
F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, Fract. Calc. Appl. Anal., 4 (2001), 153-192
##[21]
F. Mainardi, P. Paradisi , Fractional diffusive waves, J. Comput. Acoust., 9 (2001), 1417-1436
##[22]
S. Mesloub, A. Bouziani, On a class of singular hyperbolic equation with a weighted integral condition, Int. J. Math. Math. Sci., 22 (1999), 511-519
##[23]
S. Mesloub, R. Mezhoudi, M. Medjeden, A mixed problem for a parabolic equation of higher order with integral conditions, Bull. Polish Acad. Sci. Math., 50 (2002), 313-322
##[24]
K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Interscience Publication. John Wiley & Sons, Inc., , New York (1993)
##[25]
S. Momani , An explicit and numerical solutions of the fractional KdV equation, Math. Comput. Simulation, 70 (2005), 110-118
##[26]
S. Momani, Non-perturbative analytical solutions of the space- and time-fractional Burgers equations, Chaos Solitons Fractals, 28 (2006), 930-937
##[27]
S. Momani, R. Qaralleh, Numerical approximations and Padé approximants for a fractional population growth model, Appl. Math. Model., 31 (2007), 1907-1914
##[28]
S. Momani, N. Shawagfeh , Decomposition method for solving fractional Riccati differential equations, Appl. Math. Comput., 182 (2006), 1083-1092
##[29]
R. Nigmatullin, The realization of the generalized transfer equation in a medium with fractal geometry, Phys. Status Solidi B, 133 (1986), 425-430
##[30]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[31]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Gordon and Breach Science PublishersTheory and applications, Edited and with a foreword by S. M. Nikolski˘ı, Translated from the 1987 Russian original, Revised by the authors, , Yverdon (1993)
]
Sequential fractional differential equations and unification of anti-periodic and multi-point boundary conditions
Sequential fractional differential equations and unification of anti-periodic and multi-point boundary conditions
en
en
In this paper, we present a novel idea of unification of anti-periodic and multi-point boundary conditions and develop the
existence theory for sequential fractional differential equations supplemented with these new conditions. We apply fixed point
theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory to obtain the
desired results. Our results are well-illustrated with the aid of examples and correspond to some new special cases for particular
choices of parameters involved in the problem.
71
83
Ahmed
Alsaedi
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
aalsaedi@hotmail.com
Bashir
Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
bashirahmad-qau@yahoo.com
Mohammed
Aqlan
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
aqlan76@gmail.com
Sequential fractional differential equations
nonlocal
anti-periodic
multi-point
existence
fixed point.
Article.7.pdf
[
[1]
B. Ahmad, J. J. Nieto, Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative, Fract. Calc. Appl. Anal., 15 (2012), 451-462
##[2]
B. Ahmad, J. J. Nieto, Sequential fractional differential equations with three-point boundary conditions, Comput. Math. Appl., 64 (2012), 3046-3052
##[3]
B. Ahmad, J. J. Nieto, A class of differential equations of fractional order with multi-point boundary conditions, Georgian Math. J., 21 (2014), 243-248
##[4]
B. Ahmad, S. K. Ntouyas, A. Alsaedi, On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions, Chaos Solitons Fractals, 83 (2016), 234-241
##[5]
S. Aljoudi, B. Ahmad, J. J. Nieto, A. Alsaedi, A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions, Chaos Solitons Fractals, 91 (2016), 39-46
##[6]
A. Alsaedi, S. Sivasundaram, B. Ahmad, On the generalization of second order nonlinear anti-periodic boundary value problems, Nonlinear Stud., 16 (2009), 415-420
##[7]
M. H. Aqlan, A. Alsaedi, B. Ahmad, J. J. Nieto, Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions, Open Math., 14 (2016), 723-735
##[8]
M. Benchohra, N. Hamidi, J. Henderson, Fractional differential equations with anti-periodic boundary conditions, Numer. Funct. Anal. Optim., 34 (2013), 404-414
##[9]
A. Bitsadze, A. Samarskii, On some simple generalizations of linear elliptic boundary problems, Soviet Math. Dokl., 10 (1969), 398-400
##[10]
J.-F. Cao, Q.-G. Yang, Z.-T. Huang, Existence of anti-periodic mild solutions for a class of semilinear fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 277-283
##[11]
A. Granas, J. Dugundji, Fixed point theory, Springer Monographs in Mathematics, Springer-Verlag, , New York (2003)
##[12]
J. Jiang, Solvability of anti-periodic boundary value problem for coupled system of fractional p-Laplacian equation, Adv. Difference Equ., 2015 (2015 ), 1-11
##[13]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[14]
M. Klimek, Sequential fractional differential equations with Hadamard derivative, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 4689-4697
##[15]
Y.-H. Li, A.-B. Qi , Positive solutions for multi-point boundary value problems of fractional differential equations with p-Laplacian, Math. Methods Appl. Sci., 39 (2016), 1425-1434
##[16]
L. Peng, Y. Zhou, Bifurcation from interval and positive solutions of the three-point boundary value problem for fractional differential equations, Appl. Math. Comput., 257 (2015), 458-466
##[17]
D. R. Smart , Fixed point theorems, Cambridge Tracts in Mathematics, Cambridge University Press, London-New York (1980)
##[18]
J. Tariboon, T. Sitthiwirattham, S. K. Ntouyas, Existence results for fractional differential inclusions with multi-point and fractional integral boundary conditions, J. Comput. Anal. Appl., 17 (2014), 343-360
##[19]
J.-R. Wang, Y. Zhou, M. Fečkan, On the nonlocal Cauchy problem for semilinear fractional order evolution equations, Cent. Eur. J. Math., 12 (2014), 911-922
##[20]
S.-L. Xie, Y.-M. Xie, Positive solutions of a system for nonlinear singular higher-order fractional differential equations with fractional multi-point boundary conditions, Bound. Value Probl., 2016 (2016 ), 1-18
##[21]
Y. Zhou, Basic theory of fractional differential equations, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2014)
]
Well-posedness for a class of strong vector equilibrium problems
Well-posedness for a class of strong vector equilibrium problems
en
en
In this paper, we first construct a complete metric space \(\Lambda\) consisting of a class of strong vector equilibrium problems
(for short, (SVEP)) satisfying some conditions. Under the abstract framework, we introduce a notion of well-posedness for the
(SVEP), which unifies its Hadamard and Tikhonov well-posedness. Furthermore, we prove that there exists a dense \(G_{\delta}\) set Q of
\(\Lambda\) such that each (SVEP) in Q is well-posed, that is, the majority (in Baire category sense) of (SVEP) in \(\Lambda\) is well-posed. Finally,
metric characterizations on the well-posedness for the (SVEP) are given.
84
91
Yang
Yanlong
School of computer science and technology
Guizhou University
China
yylong1980@163.com
Deng
Xicai
Department of Mathematics and Computer
Guizhou Normal College
China
iamdengxicai@163.com
Xiang
Shuwen
School of computer science and technology
Guizhou University
China
shwxiang@vip.163.com
Jia
Wensheng
School of computer science and technology
Guizhou University
China
jws0505@163.com
Strong vector equilibrium problems
well-posedness
dense set
metric characterizations.
Article.8.pdf
[
[1]
C. D. Aliprantis, K. C. Border, Infinite-dimensional analysis, A hitchhiker’s guide, Second edition, Springer-Verlag, Berlin (1999)
##[2]
L. Anderlini, D. Canning, Structural stability implies robustness to bounded rationality, J. Econom. Theory, 101 (2001), 395-422
##[3]
G. Beer , On a generic optimization theorem of Petar Kenderov, Nonlinear Anal., 12 (1988), 647-655
##[4]
M. Bianchi, G. Kassay, R. Pini, Well-posedness for vector equilibrium problems, Math. Methods Oper. Res., 70 (2009), 171-182
##[5]
G.-Y. Chen, X.-X. Huang, X.-Q. Yang,/ , Vector optimization, Set-valued and variational analysis, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin (2005)
##[6]
X.-C. Deng, S.-W. Xiang, Well-posed generalized vector equilibrium problems, J. Inequal. Appl., 2014 (2014 ), 1-12
##[7]
D. Dentcheva, S. Helbig, On variational principles, level sets, well-posedness, and \(\varepsilon\)-solutions in vector optimization, J. Optim. Theory Appl., 89 (1996), 325-349
##[8]
A. L. Dontchev, T. Zolezzi, Well-posed optimization problems, Lecture Notes in Mathematics, Springer-Verlag, Berlin (1993)
##[9]
M. K. Fort, Points of continuity of semicontinuous functions, Publ. Math. Debrecen., 2 (1951), 100-102
##[10]
C. Gerth, P. Weidner, Nonconvex separation theorems and some applications in vector optimization, J. Optim. Theory Appl., 67 (1990), 297-320
##[11]
F. Giannessi (ed.), Vector variational inequalities and vector equilibria, Mathematical theories, Nonconvex Optimization and its Applications, 38. Kluwer Academic Publishers, Dordrecht (2000)
##[12]
X.-X. Huang , Extended well-posedness properties of vector optimization problems, J. Optim. Theory Appl., 106 (2000), 165-182
##[13]
X.-X. Huang, Extended and strongly extended well-posedness of set-valued optimization problems, Math. Methods Oper. Res., 53 (2001), 101-116
##[14]
X.-X. Huang, Pointwise well-posedness of perturbed vector optimization problems in a vector-valued variational principle, J. Optim. Theory Appl., 108 (2001), 671-686
##[15]
P. S. Kenderov, Most of the optimization problems have unique solution, in: B Brosowski, F. Deutsch (Eds.), Proceedings, Oberwolhfach on Parametric Optimization, in: Birkhauser International Series of Numerical Mathematics, Birkhauser, Basel, 72 (1984), 203-216
##[16]
P. S. Kenderov, N. K. Ribarska, Most of the two-person zero-sum games have unique solution , Workshop/Miniconference on Functional Analysis and Optimization, Canberra, (1988), 73–82, Proc. Centre Math. Anal. Austral. Nat. Univ., Austral. Nat. Univ., Canberra, 20 (1988), 73-82
##[17]
E. S. Levitin, B. T. Polyak, Convergence of minimizing sequences in conditional extremum problems, Dokl. Akad. Nauk SSSR, 168 (1966), 764-767
##[18]
S. J. Li, M. H. Li, Levitin-Polyak well-posedness of vector equilibrium problems, Math. Methods Oper. Res., 69 (2009), 125-140
##[19]
S. J. Li, W. Y. Zhang, Hadamard well-posed vector optimization problems, J. Global Optim., 46 (2010), 383-393
##[20]
D. T. Luc, Theory of vector optimization, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin (1989)
##[21]
R. Lucchetti , Well-posedness towards vector optimizationn, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 294 (1987), 194-207
##[22]
E. Miglierina, E. Molho, Well-posedness and convexity in vector optimization, Math. Methods Oper. Res., 58 (2003), 375-385
##[23]
E. Miglierina, E. Molho, M. Rocca, ell-posedness and scalarization in vector optimization, J. Optim. Theory Appl., 126 (2005), 391-409
##[24]
D. T. Peng, J. Yu, N. H. Xiu, Generic uniqueness of solutions for a class of vector Ky Fan inequalities, J. Optim. Theory Appl., 155 (2012), 165-179
##[25]
K.-K. Tan, J. Yu, X.-Z. Yuan, The uniqueness of saddle points, Bull. Polish Acad. Sci. Math., 43 (1995), 119-129
##[26]
A. N. Tyhonov, On the stability of the functional optimization problem, U.S.S.R. Comput. Math. Math. Phys., 6 (1966), 28-33
##[27]
J. Yu, Essential equilibria of n-person noncooperative games, J. Math. Econom., 31 (1999), 361-372
##[28]
J. Yu, D.-T. Peng, S.-W. Xiang , Generic uniqueness of equilibrium points, Nonlinear Anal., 74 (2011), 6326-6332
##[29]
J. Yu, H. Yang, C. Yu , Structural stability and robustness to bounded rationality for non-compact cases, J. Global Optim., 44 (2009), 149-157
##[30]
C. Yu, J. Yu, On structural stability and robustness to bounded rationality, Nonlinear Anal., 65 (2006), 583-592
##[31]
A. J. Zaslavski, Generic well-posedness of minimization problems with mixed continuous constraints, Nonlinear Anal., 64 (2006), 2381-2399
##[32]
A. J. Zaslavski, Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions, J. Math. Anal. Appl., 335 (2007), 962-973
##[33]
W.-B. Zhang, N.-J. Huang, D. O’Regan, Generalized well-posedness for symmetric vector quasi-equilibrium problems, J. Appl. Math., 2015 (2015 ), 1-10
]
\(\alpha\)-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces
\(\alpha\)-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces
en
en
In this paper, we introduce \(\alpha\)-proximal fuzzy contraction of type-I and II in complete fuzzy metric space and obtain some
fuzzy proximal and optimal coincidence point results. The obtained results further unify, extend and generalize some already
existing results in literature. We also provide some examples which show the validity of obtained results and a comparison is
also given which shows that contractive mappings and obtained results further generalizes already existing results in literature.
92
103
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Naeem
Saleem
Department of Mathematics
University of Management and Technology
Pakistan
naeem.saleem2@gmail.com
Mujahid
Abbas
Department of Mathematics
Department of Mathematics
King Abdulaziz University
University of Management and Technology
Saudi Arabia
Pakistan
mujahid.abbas@up.ac.za
Fuzzy metric space
\(\alpha\)-proximal fuzzy contraction of type-I
\(\alpha\)-proximal fuzzy contraction of type-II
fuzzy expansive mapping
optimal coincidence best proximity point
t-norm.
Article.9.pdf
[
[1]
M. Abbas, N. Saleem, M. De la Sen, Optimal coincidence point results in partially ordered non-Archimedean fuzzy metric spaces, Fixed Point Theory Appl., 2016 (2016 ), 1-18
##[2]
M. De la Sen, M. Abbas, N. Saleem , On optimal fuzzy best proximity coincidence points of fuzzy order preserving proximal \((\alpha,\beta)\)-lower-bounding asymptotically contractive mappings in non-Archimedean fuzzy metric spaces , SpringerPlus, 5 (2016), 1-26
##[3]
A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points , J. Math. Anal. Appl., 323 (2006), 1001-1006
##[4]
K. Fan, Extensions of two fixed point theorems of F. E. Browder , Math. Z., 112 (1969), 234-240
##[5]
A. George, P. Veeramani, On some results in fuzzy metric spaces , Fuzzy Sets and Systems, 64 (1994), 395-399
##[6]
A. George, P. Veeramani , On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365-368
##[7]
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389
##[8]
J. Gutiérrez García, S. Romaguera, Examples of non-strong fuzzy metrics, Fuzzy Sets and Systems, 162 (2011), 91-93
##[9]
N. Hussain, A. Latif, P. Salimi , Best proximity point results for modified Suzuki \(\alpha-\psi\)-proximal contractions, Fixed Point Theory Appl., 2014 (2014 ), 1-16
##[10]
M. Jleli, B. Samet, An optimization problem involving proximal quasi-contraction mappings, Fixed Point Theory Appl., 2014 (2014 ), 1-12
##[11]
I. Kramosil, J. Michàlek, Fuzzy metric and statistical metric spaces, Kybernetika (Prague), 11 (1975), 336-344
##[12]
A. Latif, M. Hezarjaribi, P. Salimi, N. Hussain, Best proximity point theorems for \(\alpha-\psi\)-proximal contractions in intuitionistic fuzzy metric spaces, J. Inequal. Appl., 2014 (2014 ), 1-19
##[13]
A. Latif, A. Ninsri, W. Sintunavarat, The \((\alpha,\beta)\)-generalized convex contractive condition with approximate fixed point results and some consequence, Fixed Point Theory Appl., 2016 (2016 ), 1-14
##[14]
C. Mongkolkeha, Y. J. Cho, P. Kumam, Best proximity points for generalized proximal C-contraction mappings in metric spaces with partial orders, J. Inequal. Appl., 2013 (2013 ), 1-12
##[15]
C. Mongkolkeha, W. Sintunavarat, Best proximity points for multiplicative proximal contraction mapping on multiplicative metric spaces, J. Nonlinear Sci. Appl., 8 (2016), 1134-1140
##[16]
M. Ozavsar, A. C. Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, ArXiv, 2012 (2012), 1-14
##[17]
Z. Raza, N. Saleem, M. Abbas, Optimal coincidence points of proximal quasi-contraction mappings in non-Archimedean fuzzy metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 3787-3801
##[18]
N. Saleem, M. Abbas, Z. Raza, Optimal coincidence best approximation solution in non-Archimedean fuzzy metric spaces, Iran. J. Fuzzy Syst., 13 (2016), 113-124
##[19]
N. Saleem, B. Ali, M. Abbas, Z. Raza, Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications, Fixed Point Theory Appl., 2015 (2015 ), 1-18
##[20]
V. Sankar Raj, P. Veeramani, Best proximity pair theorems for relatively nonexpansive mappings, Appl. Gen. Topol., 10 (2009), 21-28
##[21]
B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334
##[22]
T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., 71 (2009), 2918-2926
##[23]
C. Vetro, P. Salimi, Best proximity point results in non-Archimedean fuzzy metric spaces, Fuzzy Inf. Eng., 5 (2013), 417-429
]
Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces
Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces
en
en
In this paper, we solve the quadratic \(\rho\)-functional inequalities
\[\|f(x+y)+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|<1\), and\[\|4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(f(x+y)+f(x-y)-2f(x)-2f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|<1\).
Using the direct method, we prove the Hyers-Ulam stability of the quadratic \(\rho\)-functional inequalities (1) and (2) in \(\beta\)-
homogeneous complex Banach spaces.
104
110
Yuanfeng
Park
Department of Mathematics, Research Institute for Natural Sciences
Hanyang University
Korea
baak@hanyang.ac.kr
Yinhua
Lu
Department of Mathematics, School of Science
Department of Mathematics
ShenYang University of Technology
Zhejiang University
P. R. China
P. R. China
lvgang1234@hanmail.net
Gang
Cui
Department of Mathematics
Yanbian University
P. R. China
cuiyh@ybu.edu.cn
Choonkil
Jin
Department of Mathematics
Yanbian University
P. R. China
yfjim@ybu.edu.cn
Hyers-Ulam stability
\(\beta\)-homogeneous space
quadratic \(\rho\)-functional inequality.
Article.10.pdf
[
[1]
T. Aoki , On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[2]
P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 (1984), 76-86
##[3]
P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
##[4]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27 (1941), 222-224
##[5]
C.-K. Park, Additive \(\rho\)-functional inequalities and equations, J. Math. Inequal., 9 (2015), 17-26
##[6]
C.-K. Park , Additive \(\rho\)-functional inequalities in non-Archimedean normed spaces, J. Math. Inequal., 9 (2015), 397-407
##[7]
C.-K. Park, K. Ghasemi, S. G. Ghaleh, S. Y. Jang, Approximate \(\eta\)-Jordan \(*\)-homomorphisms in \(C^*\)-algebras, J. Comput. Anal. Appl., 15 (2013), 365-368
##[8]
C.-K. Park, A. Najati, S. Y. Jang , Fixed points and fuzzy stability of an additive-quadratic functional equation, J. Comput. Anal. Appl., 15 (2013), 452-462
##[9]
T. M. Rassias, On the stability of the linear mapping in Banach spaces , Proc. Amer. Math. Soc., 72 (1978), 297-300
##[10]
S. Rolewicz , Metric linear spaces, Monografie Matematyczne , Tom, [Mathematical Monographs] PWN-Polish Scientific Publishers, Warsaw (1972)
##[11]
S. Shagholi, M. E. Gordji, M. Bavand Savadkouhi, Nearly ternary cubic homomorphism in ternary Fréchet algebras, J. Comput. Anal. Appl., 13 (2011), 1106-1114
##[12]
S. Shagholi, M. E. Gordji, M. Bavand Savadkouhi , Stability of ternary quadratic derivation on ternary Banach algebras, J. Comput. Anal. Appl., 13 (2011), 1097-1105
##[13]
D. Y. Shin, C.-K. Park, S. Farhadabadi, On the superstability of ternary Jordan \(C^*\)-homomorphisms, J. Comput. Anal. Appl., 16 (2014), 964-973
##[14]
D. Y. Shin, C.-K. Park, S. Farhadabadi, Stability and superstability of \(J^*\)-homomorphisms and \(J^*\)-derivations for a generalized Cauchy-Jensen equation, J. Comput. Anal. Appl., 17 (2014), 125-134
##[15]
F. Skof, Proprietà locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano, 53 (1983), 113-129
##[16]
S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers, New York-London (1960)
]
Application of double Laplace decomposition method for solving singular one dimensional system of hyperbolic equations
Application of double Laplace decomposition method for solving singular one dimensional system of hyperbolic equations
en
en
In this paper, the Adomain decomposition methods and double Laplace transform methods are combined to study linear
and nonlinear singular one dimensional system of hyperbolic equations. In addition, we check the convergence of double
Laplace transform decomposition method applied to our problems. Furthermore, we illustrate our proposed methods by using
some examples.
111
121
Hassan Eltayeb
Gadain
Mathematics Department, College of Science
King Saud University
Saudi Arabia
hgadain@ksu.edu.sa
Double Laplace transform
inverse Laplace transform
system of hyperbolic equations.
Article.11.pdf
[
[1]
K. Abbaoui, Y. Cherruault, Convergence of Adomian’s method applied to differential equations, Comput. Math. Appl., 28 (1994), 103-109
##[2]
K. Abbaoui, Y. Cherruault , Convergence of Adomian’s method applied to nonlinear equations, Math. Comput. Modelling, 20 (1994), 69-73
##[3]
F. M. Allan, K. Al-Khaled , An approximation of the analytic solution of the shock wave equation, J. Comput. Appl. Math., 192 (2006), 301-309
##[4]
A. Atangana, S. C. Oukouomi Noutchie, On multi-Laplace transform for solving nonlinear partial differential equations with mixed derivatives, Math. Probl. Eng., 2014 (2014 ), 1-9
##[5]
E. Babolian, J. Biazar, On the order of convergence of Adomian method, Appl. Math. Comput., 130 (2002), 383-387
##[6]
Y. Cherruault, G. Saccomandi, B. Some, New results for convergence of Adomian’s method applied to integral equations, Math. Comput. Modelling, 16 (1992), 85-93
##[7]
S. M. El-Sayed, D. Kaya, On the numerical solution of the system of two-dimensional Burgers’ equations by the decomposition method, Appl. Math. Comput., 158 (2004), 101-109
##[8]
H. Eltayeb, A. Kılıçman, A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform, Appl. Math. Lett., 21 (2008), 1324-1329
##[9]
I. Hashim, M. S. M. Noorani, M. R. Said Al-Hadidi, Solving the generalized Burgers-Huxley equation using the Adomian decomposition method, Math. Comput. Modelling, 43 (2006), 1404-1411
##[10]
D. Kaya, I. E. Inan, A convergence analysis of the ADM and an application, Appl. Math. Comput., 161 (2005), 1015-1025
##[11]
D. Kaya, I. E. Inan, A numerical application of the decomposition method for the combined KdV-MKdV equation, Appl. Math. Comput., 168 (2005), 915-926
##[12]
S. A. Khuri, A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. Appl. Math., 1 (2001), 141-155
##[13]
A. Kılıçman, H. Eltayeb, A note on defining singular integral as distribution and partial differential equations with convolution term, Math. Comput. Modelling, 49 (2009), 327-336
##[14]
A. Kılıçman, H. E. Gadain, On the applications of Laplace and Sumudu transforms, J. Franklin Inst., 347 (2010), 848-862
##[15]
T. Mavoungou, Y. Cherruault, Numerical study of Fisher’s equation by Adomian’s method, Math. Comput. Modelling, 19 (1994), 89-95
##[16]
S. S. Ray , A numerical solution of the coupled sine-Gordon equation using the modified decomposition method, Appl. Math. Comput., 175 (2006), 1046-1054
##[17]
N. H. Sweilam , Harmonic wave generation in non linear thermoelasticity by variational iteration method and Adomian’s method, J. Comput. Appl. Math., 207 (2007), 64-72
##[18]
E. Yusufoğlu, Numerical solution of Duffing equation by the Laplace decomposition algorithm, Appl. Math. Comput., 177 (2006), 572-580
]
Integral inequalities of extended Simpson type for (\(\alpha,m\))-varepsilon-convex functions
Integral inequalities of extended Simpson type for (\(\alpha,m\))-varepsilon-convex functions
en
en
In the paper, the authors establish some integral inequalities of extended Simpson type for \((\alpha,m)-\varepsilon\)-convex functions.
122
129
Jun
Zhang
College of Computer Science and Technology
College of Computer Science and Technology
Jilin University
Inner Mongolia University for Nationalities
China
China
Zhangjun728@163.com
Zhi-Li
Pei
College of Computer Science and Technology
Inner Mongolia University for Nationalities
China
zhilipei@sina.com
Gao-Chao
Xu
College of Computer Science and Technology
Jilin University
China
xugc@jlu.edu.cn
Xiao-Hui
Zou
College of Computer Science and Technology
Jilin University
China
496072945@qq.com
Feng
Qi
Department of Mathematics, College of Science
Institute of Mathematics
Tianjin Polytechnic University
Henan Polytechnic University
China
China
qifeng618@gmail.com;qifeng618@hotmail.com
Integral inequality
extended Simpson type
\((\alpha،m)-\varepsilon\)-convex function
Article.12.pdf
[
[1]
S. S. Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95
##[2]
S. S. Dragomir, G. Toader, Some inequalities for m-convex functions, Studia Univ. Babe-Bolyai Math., 38 (1993), 21-28
##[3]
J. Hua, B.-Y. Xi, F. Qi , Inequalities of Hermite-Hadamard type involving an s-convex function with applications, Appl. Math. Comput., 246 (2014), 752-760
##[4]
D. H. Hyers, S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc., 3 (1952), 821-828
##[5]
U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147 (2004), 137-146
##[6]
M. Klaričić Bakula, M. E. Özdemir, J. Pečarić, Hadamard type inequalities for m-convex and \((\alpha,m)\)-convex functions, JIPAM. J. Inequal. Pure Appl. Math., 9 (2008), 1-12
##[7]
V. G. Miheşan, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj- Napoca, Romania, (1993), -
##[8]
C. E. M. Pearce, J. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formul, Appl. Math. Lett., 13 (2000), 51-55
##[9]
F. Qi, B.-Y. Xi, Some Hermite-Hadamard type inequalities for geometrically quasi-convex functions, Proc. Indian Acad. Sci. Math. Sci., 124 (2014), 333-342
##[10]
F. Qi, T.-Y. Zhang, B.-Y. Xi, Hermite-Hadamard-type integral inequalities for functions whose first derivatives are convex, Reprint of Ukraïn. Mat. Zh., 67 (2015), 555–567, Ukrainian Math. J., 67 (2015), 625-640
##[11]
G. Toader, Some generalizations of the convexity , Proceedings of the colloquium on approximation and optimization, Cluj-Napoca, (1985), 329–338, Univ. Cluj-Napoca, Cluj-Napoca (1985)
##[12]
B.-Y. Xi, F. Qi, Hermite-Hadamard type inequalities for geometrically r-convex functions, Studia Sci. Math. Hungar., 51 (2014), 530-546
##[13]
B.-Y. Xi, F. Qi, Inequalities of Hermite-Hadamard type for extended s-convex functions and applications to means, J. Nonlinear Convex Anal., 16 (2015), 873-890
##[14]
B.-Y. Xi, S.-H. Wang, F. Qi, Some inequalities for (h,m)-convex functions, J. Inequal. Appl., 2014 (2014 ), 1-12
##[15]
B.-Y. Xi, T.-Y. Zhang, F. Qi, Some inequalities of Hermite–Hadamard type for m-harmonic-arithmetically convex functions, ScienceAsia, 41 (2015), 357-361
]
The viscosity approximation forward-backward splitting method for solving quasi inclusion problems in Banach spaces
The viscosity approximation forward-backward splitting method for solving quasi inclusion problems in Banach spaces
en
en
In this paper, we introduce viscosity approximation forward-backward splitting method for an accretive operator and an
m-accretive operator in Banach spaces. The strong convergence of this viscosity method is proved under certain assumptions
imposed on the sequence of parameters. Applications to the minimization optimization problem and the linear inverse problem
are included. The results presented in the paper extend and improve some recent results announced in the current literature.
130
140
Fu Hai
Zhao
School of Science
South West University of Science and Technology
P. R. China
zhaofuhai@swust.edu.cn
Li
Yang
School of Science
South West University of Science and Technology
P. R. China
yangli@swust.edu.cn
Accretive operator
viscosity approximation
Banach space
splitting method
forward-backward algorithm.
Article.13.pdf
[
[1]
H. Attouch, Viscosity solutions of minimization problems, SIAM J. Optim., 6 (1996), 769-806
##[2]
J. B. Baillon, G. Haddad , Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones, (French) Israel J. Math., 26 (1977), 137-150
##[3]
D. P. Bertsekas, J. N. Tsitsiklis, Parallel and distributed computation: numerical methods, Prentice-Hall, Englewood Cliffs, NJ, (1989); republished in 1997 by Athena Scientific, MA (1997)
##[4]
H. Brézis, P.-L. Lions, Produits infinis de résolvantes, (French) Israel J. Math., 29 (1978), 329-345
##[5]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
##[6]
G. H.-G. Chen, R. T. Rockafellar, Convergence rates in forward-backward splitting, SIAM J. Optim., 7 (1997), 421-444
##[7]
C. Chidume , Geometric properties of Banach spaces and nonlinear iterations, Lecture Notes in Mathematics, Springer- Verlag London, Ltd., London (2009)
##[8]
P. Cholamjiak, A generalized forward-backward splitting method for solving quasi inclusion problems in Banach spaces, Numer. Algorithms, 71 (2016), 915-932
##[9]
I. Cioranescu, Geometry of Banach spaces, duality mappings and nonlinear problems, Kluwer Academic Publishers GroupMathematics and its Applications,, Dordrecht (1990)
##[10]
P. L. Combettes, Iterative construction of the resolvent of a sum of maximal monotone operators, J. Convex Anal., 16 (2009), 727-748
##[11]
P. L. Combettes, V. R.Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168-1200
##[12]
J. Douglas Jr., H. H. Rachford, On the numerical solution of heat conduction problems in two and three space variables, Trans. Amer. Math. Soc., 82 (1956), 421-439
##[13]
J. C. Dunn, Convexity, monotonicity, and gradient processes in Hilbert space, J. Math. Anal. Appl., 53 (1976), 145-158
##[14]
O. Güler, On the convergence of the proximal point algorithm for convex minimization, SIAM J. Control Optim., 29 (1991), 403-419
##[15]
S.-N. He, C.-P. Yang, Solving the variational inequality problem defined on intersection of finite level sets, Abstr. Appl. Anal., 2013 (2013 ), 1-8
##[16]
P.-L. Lions, B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal., 16 (1979), 964-979
##[17]
G. López, V. Martín-Márquez, F.-H. Wang, H.-K. Xu, Forward-backward splitting methods for accretive operators in Banach spaces, Abstr. Appl. Anal., 2012 (2012 ), 1-25
]
Existence of mild solutions for a class of non-autonomous evolution equations with nonlocal initial conditions
Existence of mild solutions for a class of non-autonomous evolution equations with nonlocal initial conditions
en
en
Using the techniques of measures of noncompactness and Schauder fixed point theorem, we present some existence results
for mild solutions of a class of nonlocal evolution equations involving causal operators. Moreover, we obtain the compactness
of the set of global mild solutions. An example is given to show the efficiency and usefulness of the results.
141
153
Tahira
Jabeen
Abdus Salam School of Mathematical Sciences
GC University
Pakistan
tahirajabeen14@gmail.com
Vasile
Lupulescu
Constantin Brancusi University
Romania
vasile@utgjiu.ro
Non-autonomous evolution equation
nonlocal condition
evolution semigroups
causal operator
mild solution.
Article.14.pdf
[
[1]
R. P. Agarwal, S. Arshad, V. Lupulescu, D. O’Regan, Evolution equations with causal operators, Differ. Equ. Appl., 7 (2015), 15-26
##[2]
R. P. Agarwal, J. Banaś, B. C. Dhage, S. D. Sarkate, Attractivity results for a nonlinear functional integral equation, Georgian Math. J., 18 (2011), 1-19
##[3]
S. Aizicovici, H.-W. Lee, Nonlinear nonlocal Cauchy problems in Banach spaces, Appl. Math. Lett., 18 (2005), 401-407
##[4]
S. Aizicovici, M. McKibben, Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Anal., 39 (2000), 649-668
##[5]
S. Aizicovici, V. Staicu, Multivalued evolution equations with nonlocal initial conditions in Banach spaces, NoDEA Nonlinear Differential Equations Appl., 14 (2007), 361-376
##[6]
K. Balachandran, J. J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Anal., 72 (2010), 4587-4593
##[7]
D. Baleanu, H. Jafari, H. Khan, S. J. Johnston, Results for mild solution of fractional coupled hybrid boundary value problems, Open Math., 13 (2015), 601-608
##[8]
M. Benchohra, E. P. Gatsori, S. K. Ntouyas, Existence results for semi-linear integrodifferential inclusions with nonlocal conditions, Rocky Mountain J. Math., 34 (2004), 833-848
##[9]
M. Benchohra, J. Henderson, S. K. Ntouyas, Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces, J. Math. Anal. Appl., 263 (2001), 763-780
##[10]
M. Benchohra, G. M. N’Guérékata, D. Seba, Measure of noncompactness and nondensely defined semilinear functional differential equations with fractional order, Cubo, 12 (2010), 35-48
##[11]
I. Benedetti, N. V. Loi, L. Malaguti, Nonlocal problems for differential inclusions in Hilbert spaces, Set-Valued Var. Anal., 22 (2014), 639-656
##[12]
I. Benedetti, L. Malaguti, V. Taddei, I. I. Vrabie, Semilinear delay evolution equations with measures subjected to nonlocal initial conditions, Ann. Mat. Pura Appl., 195 (2016), 1639-1658
##[13]
L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162 (1991), 494-505
##[14]
L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 40 (1991), 11-19
##[15]
T. Cardinali, R. Precup, P. Rubbioni, A unified existence theory for evolution equations and systems under nonlocal conditions, J. Math. Anal. Appl., 432 (2015), 1039-1057
##[16]
T. Cardinali, P. Rubbioni, On the existence of mild solutions of semilinear evolution differential inclusions, J. Math. Anal. Appl., 308 (2005), 620-635
##[17]
T. Cardinali, P. Rubbioni, Corrigendum and addendum to ''On the existence of mild solutions of semilinear evolution differential inclusions'', [J. Math. Anal. Appl., 308 (2005), 620–635], J. Math. Anal. Appl., 438 (2016), 514-517
##[18]
P.-Y. Chen, Y.-X. Li, Q. Li, Existence of mild solutions for fractional evolution equations with nonlocal initial conditions, Ann. Polon. Math., 110 (2014), 13-24
##[19]
P.-Y. Chen, Y.-X. Li , Nonlocal problem for fractional evolution equations of mixed type with the measure of noncompactness, Abstr. Appl. Anal., 2013 (2013), 1-12
##[20]
C. Corduneanu, Functional equations with causal operators, Stability and Control: Theory, Methods and Applications, Taylor & Francis, London (2002)
##[21]
R. F. Curtain, H. Zwart, An introduction to infinite-dimensional linear systems theory, Texts in Applied Mathematics, Springer-Verlag,, New York (1995)
##[22]
A. Debbouche, D. Baleanu, R. P. Agarwal, Nonlocal nonlinear integrodifferential equations of fractional orders, Bound. Value Probl., 2012 (2012 ), 1-10
##[23]
R. E. Edwards, Functional analysis, Theory and applications, Holt, Rinehart and Winston, New York-Toronto- London (1965)
##[24]
Z.-B. Fan, G. Li, Existence results for semilinear differential equations with nonlocal and impulsive conditions, J. Funct. Anal., 258 (2010), 1709-1727
##[25]
X.-L. Fu, K. Ezzinbi, Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear Anal., 54 (2003), 215-227
##[26]
M. A. E. Herzallah, D. Baleanu, Existence of a periodic mild solution for a nonlinear fractional differential equation, Comput. Math. Appl., 64 (2012), 3059-3064
##[27]
L.-Y. Hu, Y. Ren, R. Sakthivel, Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays, Semigroup Forum, 79 (2009), 507-514
##[28]
S.-C. Ji, G. Li, Existence results for impulsive differential inclusions with nonlocal conditions, Comput. Math. Appl., 62 (2011), 1908-1915
##[29]
J.-F. Jiang, D.-Q. Cao, H.-T. Chen, The fixed point approach to the stability of fractional differential equations with causal operators, Qual. Theory Dyn. Syst., 15 (2016), 3-18
##[30]
J.-F. Jiang, C. F. Li, D.-Q. Cao, H.-T. Chen, Existence and uniqueness of solution for fractional differential equation with causal operators in Banach spaces, Mediterr. J. Math., 12 (2015), 751-769
##[31]
M. Kamenskii, V. Obukhovskii, P. Zecca, Condensing multivalued maps and semilinear differential inclusions in Banach spaces, De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter & Co., Berlin (2001)
##[32]
T. D. Ke, V. Obukhovskii, N.-C. Wong, J.-C. Yao, On semilinear integro-differential equations with nonlocal conditions in Banach spaces, Abstr. Appl. Anal., 2012 (2012 ), 1-26
##[33]
M. Kisielewicz, Multivalued differential equations in separable Banach spaces, J. Optim. Theory Appl., 37 (1982), 231-249
##[34]
K. Kuratowski, Sur les espaces complets, Fund. Math., 15 (1930), 301-309
##[35]
V. G. Kurbatov, Functional-differential operators and equations, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht (1999)
##[36]
V. Lakshmikantham, S. Leela, Z. Drici, F. A. McRae, Theory of causal differential equations, Atlantis Studies in Mathematics for Engineering and Science, Atlantis Press, Paris; World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2009)
##[37]
J. Liang, J. H. Liu, T.-J. Xiao, Nonlocal Cauchy problems for nonautonomous evolution equations, Commun. Pure Appl. Anal., 5 (2006), 529-535
##[38]
Y. P. Lin, J. H. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal., 26 (1996), 1023-1033
##[39]
Q. Liu, R. Yuan, Existence of mild solutions for semilinear evolution equations with non-local initial conditions, Nonlinear Anal., 71 (2009), 4177-4184
##[40]
A. Lunardi, Analytic semigroups and optimal regularity in parabolic problems, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Verlag, Basel (1995)
##[41]
V. Lupulescu, Causal functional differential equations in Banach spaces, Nonlinear Anal., 69 (2008), 4787-4795
##[42]
M. Mahdavi, Y.-Z. Li , Linear and quasilinear equations with abstract Volterra operators, Volterra equations and applications, Arlington, TX, (1996), 325–330, Stability Control Theory Methods Appl., Gordon and Breach, Amsterdam (2000)
##[43]
G. M. Mophou, Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Anal., 72 (2010), 1604-1615
##[44]
G. M. Mophou, G. M. N’Guérékata, Existence of the mild solution for some fractional differential equations with nonlocal conditions, Semigroup Forum, 79 (2009), 315-322
##[45]
G. M. Mophou, G. M. N’Guérékata, Mild solutions for semilinear fractional differential equations, Electron. J. Differential Equations, 2009 (2009 ), 1-9
##[46]
G. M. N’Guérékata, A Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear Anal., 70 (2009), 1873-1876
##[47]
S. K. Ntouyas, P. Ch. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl., 210 (1997), 679-687
##[48]
A. Paicu, I. I. Vrabie, A class of nonlinear evolution equations subjected to nonlocal initial conditions, Nonlinear Anal., 72 (2010), 4091-4100
##[49]
N. S. Papageorgiou, Mild solutions of semilinear evolution inclusions and optimal control, Indian J. Pure Appl. Math., 26 (1995), 189-216
##[50]
A. Pazy , Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, Springer-Verlag, New York (1983)
##[51]
H. Tanabe, Equations of evolution, Translated from the Japanese by N. Mugibayashi and H. Haneda, Monographs and Studies in Mathematics, Pitman (Advanced Publishing Program), Boston, Mass.-London (1979)
##[52]
I. I. Vrabie , \(C_0\)-semigroups and applications, North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam (2003)
##[53]
R.-N. Wang, K. Ezzinbi, P.-X. Zhu, Non-autonomous impulsive Cauchy problems of parabolic type involving nonlocal initial conditions, J. Integral Equations Appl., 26 (2014), 275-299
##[54]
J.-R. Wang, Y. Zhou, M. Fečkan, Abstract Cauchy problem for fractional differential equations, Nonlinear Dynam., 71 (2013), 685-700
##[55]
S. Xie, Existence of solutions for nonlinear mixed type integrodifferential functional evolution equations with nonlocal conditions, Abstr. Appl. Anal., 2012 (2012 ), 1-11
##[56]
X.-M. Xue, Nonlocal nonlinear differential equations with a measure of noncompactness in Banach spaces, Nonlinear Anal., 70 (2009), 2593-2601
##[57]
A. Yagi, Abstract parabolic evolution equations and their applications, Springer Monographs in Mathematics, Springer- Verlag, Berlin (2010)
##[58]
Y.-L. Yang, J.-R. Wang, On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces, Opuscula Math., 31 (2011), 443-455
##[59]
T. Zhu, C. Song, G. Li, Existence of mild solutions for abstract semilinear evolution equations in Banach spaces, Nonlinear Anal., 75 (2012), 177-181
]
Simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive mappings
Simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive mappings
en
en
In this paper, we investigate a new simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive
mappings in real Hilbert spaces and obtain a strong convergence result with no compactness assumptions on the spaces
or the mappings and with no extra conditions on the fixed point sets. The results obtained in this paper generalize and improve
the recent ones announced by many others.
154
165
Yaqin
Wang
Department of Mathematics
Shaoxing University
China
wangyaqin0579@126.com
Tae Hwa
Kim
Department of Applied Mathematics, College of Natural Sciences
Pukyong National University
Republic of Korea
taehwa1225@gmail.com
Split equality fixed-point problem
demicontractive mapping
strong convergence
iterative algorithm.
Article.15.pdf
[
[1]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453
##[2]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov , A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353-2365
##[3]
Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
##[4]
Y. Censor, A. Segal , The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587-600
##[5]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[6]
P. E. Maingé, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), 899-912
##[7]
G. Marino, H.-K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl., 329 (2007), 336-346
##[8]
A. Moudafi, Second-order differential proximal methods for equilibrium problems, JIPAM. J. Inequal. Pure Appl. Math., 4 (2003), 1-7
##[9]
A. Moudafi , A relaxed alternating CQ-algorithm for convex feasibility problems, Nonlinear Anal., 79 (2013), 117-121
##[10]
A. Moudafi , Alternating CQ-algorithms for convex feasibility and split fixed-point problems, J. Nonlinear Convex Anal., 15 (2014), 809-818
##[11]
A. Moudafi, E. Al-Shemas, Simultaneous iterative methods for split equality problem, Trans. Math. Program. Appl., 1 (2013), 1-11
##[12]
Y. Shehu, F. U. Ogbuisi, An iterative algorithm for approximating a solution of split common fixed point problem for demi-contractive maps, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 23 (2016), 205-216
##[13]
W. Takahashi, Nonlinear functional analysis, Yokohama Publishers, Yokohama, Japan (2000)
##[14]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[15]
Y.-H. Yao, R. P. Agarwal, M. Postolache, Y.-C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., 2014 (2014 ), 1-14
##[16]
Y.-H. Yao, M. Postolache, Y.-C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory Appl., 2013 (2013 ), 1-12
##[17]
Y.-H. Yao, J. Wu, Y.-C. Liou, Regularized methods for the split feasibility problem, Abstr. Appl. Anal., 2012 (2012 ), 1-13
##[18]
J. Zhao, S.-N. He, Simultaneous iterative algorithms for the split common fixed-point problem governed by quasinonexpansive mappings, J. Nonlinear Convex Anal., (accepted), -
]
Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients
Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients
en
en
The paper is devoted to solve multidimensional backward doubly stochastic differential equations under integral non-
Lipschitz conditions in general spaces. By stochastic analysis and constructing approximation sequence, a new set of sufficient
conditions for multidimensional backward doubly stochastic differential equations is obtained. The results generalize the recent
results on this issue. Finally, an example is given to illustrate the advantage of the main results.
166
174
Pengju
Duan
School of Mathematics and Statistics
Suzhou University
China
pjduan1981@hotmail.com
Backward doubly stochastic differential equations
existence and uniqueness
integral non-Lipschitz.
Article.16.pdf
[
[1]
N. El-Karoui, S. Hamadéne, BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations, Stochastic Process. Appl., 107 (2003), 145-169
##[2]
N. El-Karoui, S. Peng, M. C. Quenez, Backward stochastic differential equations in finance, Math. Finance, 7 (1997), 1-71
##[3]
N. El-Karoui, M. C. Quenez, Non-linear pricing theory and backward stochastic differential equations, Financial mathematics, Bressanone, (1996), 191–246, Lecture Notes in Math., 1656, Springer, Berlin (1997)
##[4]
S.-J. Fan, L. Jiang, Multidimensional BSDEs with weak monotonicity and general growth generators, Acta Math. Sin. (Engl. Ser.), 23 (2013), 1885-1906
##[5]
S.-J. Fan, L. Jiang, M. Davison, Existence and uniqueness result for multidimensional BSDEs with generators of Osgood type, Front. Math. China, 4 (2013), 811-824
##[6]
S. Hamadène, Multidimensional backward stochastic differential equations with uniformly continuous coefficients, Bernoulli, 9 (2003), 517-534
##[7]
S. Hamadène, J.-P. Lepeltier, Zero-sum stochastic differential games and backward equations, Systems Control Lett., 24 (1995), 259-263
##[8]
L.-Y. Hu, Reflected backward doubly stochastic differential equations driven by a Lévy process with stochastic Lipschitz condition, Appl. Math. Comput., 219 (2012), 1153-1157
##[9]
Y. Hu, S.-J. Tang, Multi-dimensional backward stochastic differential equations of diagonally quadratic generators, Stochastic Process. Appl., 126 (2016), 1066-1086
##[10]
J. P. Lepeltier, J. San Martin, Backward stochastic differential equations with continuous coefficient, Statist. Probab. Lett, 32 (1997), 425-430
##[11]
Q. Lin, A class of backward doubly stochastic differential equations with non-Lipschitz coefficients, Statist. Probab. Lett., 79 (2009), 2223-2229
##[12]
Q. Lin, A generalized existence theorem of backward doubly stochastic differential equations, Acta Math. Sin. (Engl. Ser.), 26 (2010), 1525-1534
##[13]
X.-R. Mao, Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Process. Appl., 58 (1995), 281-292
##[14]
É. Pardoux, S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14 (1990), 55-61
##[15]
É. Pardoux, S. G. Peng, Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Related Fields, 98 (1994), 209-227
##[16]
Y.-F. Shi, Y.-L. Gu, K. Liu, Comparison theorems of backward doubly stochastic differential equations and applications, Stoch. Anal. Appl., 23 (2005), 97-110
##[17]
X. F. Wang, L. Jiang, J. J. Ma, Multidimensional backward doubly stochastic differential equations with generators of Osgood type, (Chinese) J. Shandong Univ. Nat. Sci., 50 (2015), 24-33
]
On alternating direction method for solving variational inequality problems with separable structure
On alternating direction method for solving variational inequality problems with separable structure
en
en
We present an alternating direction scheme for the separable constrained convex programming problem. The predictor
is obtained via solving two sub-variational inequalities in a parallel wise at each iteration. The new iterate is obtained by a
projection type method along a new descent direction. The new direction is obtained by combining the descent directions using
by He [B.-S. He, Comput. Optim. Appl., 42 (2009), 195–212] and Jiang and Yuan [Z.-K. Jiang, X.-M. Yuan, J. Optim. Theory
Appl., 145 (2010), 311–323]. Global convergence of the proposed method is proved under certain assumptions. We also report
some numerical results to illustrate the efficiency of the proposed method.
175
185
Abdellah
Bnouhachem
Laboratoire d’Ingénierie des Systémes et Technologies de l’Information, ENSA
Ibn Zohr University
Morocco
babedallah@yahoo.com
Fatimazahra
Benssi
Laboratoire d’Ingénierie des Systémes et Technologies de l’Information, ENSA
Ibn Zohr University
Morocco
Abdelouahed
Hamdi
Department of Mathematics, Statistics and Physics College of Arts and Sciences
Qatar University
Qatar
abhamdi@qu.edu.qa
Variational inequalities
monotone operator
projection method
alternating direction method.
Article.17.pdf
[
[1]
A. Bnouhachem, On LQP alternating direction method for solving variational inequality problems with separable structure, J. Inequal. Appl., 2014 (2014 ), 1-15
##[2]
A. Bnouhachem, Q. H. Ansari, A descent LQP alternating direction method for solving variational inequality problems with separable structure, Appl. Math. Comput., 246 (2014), 519-532
##[3]
A. Bnouhachem, H. Benazza, M. Khalfaoui, An inexact alternating direction method for solving a class of structured variational inequalities, Appl. Math. Comput., 219 (2013), 7837-7846
##[4]
A. Bnouhachem, A. Hamdi , Parallel LQP alternating direction method for solving variational inequality problems with separable structure, J. Inequal. Appl., 2014 (2014 ), 1-14
##[5]
A. Bnouhachem, M. H. Xu, An inexact LQP alternating direction method for solving a class of structured variational inequalities, Comput. Math. Appl., 67 (2014), 671-680
##[6]
G. Chen, M. Teboulle, A proximal-based decomposition method for convex minimization problems, Math. Programming, 64 (1994), 81-101
##[7]
J. Eckstein, Some saddle-function splitting methods for convex programming, Optim. Methods Softw., 4 (1994), 75-83
##[8]
J. Eckstein, D. B. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Programming, 55 (1992), 293-318
##[9]
J. Eckstein, M. Fukushima, Some reformulations and applications of the alternating direction method of multipliers, Large scale optimization, Gainesville, FL, (1993), 115–134, Kluwer Acad. Publ., Dordrecht (1994)
##[10]
F. Facchinei, J.-S. Pang, Finite-dimensional variational inequalities and complementarity problems, I and II , Springer Series in Operations Research, Springer-Verlag, New York (2003)
##[11]
M. Fortin, R. Glowinski, Augmented Lagrangian methods: Applications to the numerical solution of boundary value problems, Translated from the French by B. Hunt and D. C. Spicer, Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam (1983)
##[12]
D. Gabay , Applications of the method of multipliers to variational inequalities, Augmented Lagrange Methods: Applications to the Solution of Boundary-valued Problems, (eds. M. Fortin and R. Glowinski), Studies in Mathematics and Its Applications, Amsterdam, The Netherlands, 15 (1983), 299-331
##[13]
D. Gabay, B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Comput. Math. Appl., 2 (1976), 17-40
##[14]
R. Glowinski, P. Le Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1989)
##[15]
A. Hamdi, S. K. Mishra, Decomposition methods based on augmented Lagrangians: a survey, Topics in nonconvex optimization, Springer Optim. Appl., Nonconvex Optim. Appl., Springer, New York, 50 (2011), 175-203
##[16]
A. Hamdi, A. A. Mukheimer, Modified Lagrangian methods for separable optimization problems, Abstr. Appl. Anal., 2012 (2012 ), 1-20
##[17]
B.-S. He, L.-Z. Liao, D.-R. Han, H. Yang, A new inexact alternating directions method for monotone variational inequalities, Math. Programming, 92 (2002), 103-118
##[18]
B.-S. He, Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities, Comput. Optim. Appl., 42 (2009), 195-212
##[19]
B.-S. He, M. Tao, X.-M. Yuan, Alternating direction method with Gaussian back substitution for separable convex programming, SIAM J. Optim., 22 (2012), 313-340
##[20]
B.-S. He, H. Yang, Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities, Oper. Res. Lett., 23 (1998), 151-161
##[21]
L. S. Hou, On the \(O(1/t)\) convergence rate of the parallel descent-like method and parallel splitting augmented Lagrangian method for solving a class of variational inequalities, Appl. Math. Comput., 219 (2013), 5862-5869
##[22]
Z.-K. Jiang, A. Bnouhachem, A projection-based prediction-correction method for structured monotone variational inequalities, Appl. Math. Comput., 202 (2008), 747-759
##[23]
Z.-K. Jiang, X.-M. Yuan, New parallel descent-like method for solving a class of variational inequalities, J. Optim. Theory Appl., 145 (2010), 311-323
##[24]
M. Li, A hybrid LQP-based method for structured variational inequalities, Int. J. Comput. Math., 89 (2012), 1412-1425
##[25]
M. Tao, X.-M. Yuan, On the \(O(1/t)\) convergence rate of alternating direction method with logarithmic-quadratic proximal regularization, SIAM J. Optim., 22 (2012), 1431-1448
##[26]
P. Tseng, Alternating projection-proximal methods for convex programming and variational inequalities, SIAM J. Optim., 7 (1997), 951-965
##[27]
K. Wang, L.-L. Xu, D.-R. Han, A new parallel splitting descent method for structured variational inequalities, J. Ind. Manag. Optim., 10 (2014), 461-476
##[28]
X.-M. Yuan, M. Li , An LQP-based decomposition method for solving a class of variational inequalities, SIAM J. Optim., 21 (2011), 1309-1318
]
Revisit of identities for Apostol-Euler and Frobenius-Euler numbers arising from differential equation
Revisit of identities for Apostol-Euler and Frobenius-Euler numbers arising from differential equation
en
en
In this paper, we study differential equation arising from the generating function of Apostol-Euler and Frobenius-Euler
numbers. In addition, we revisit some identities of Apostol-Euler and Frobenius-Euler numbers which are derived from differential
equations.
186
191
Taekyun
Kim
Department of Mathematics
Department of Mathematics
College of Science Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Gwan-Woo
Jang
Department of Mathematics
Kwangwoon University
Republic of Korea
jgw5687@naver.com
Jong Jin
Seo
Department of Mathematics
Department of Mathematics
Kwangwoon University
Pukyung National University
Republic of Korea
Republic of Korea
seo2011@pknu.ac.kr
Nonlinear differential equations
Apostol-Euler numbers
Frobenius-Euler numbers.
Article.18.pdf
[
[1]
A. Bayad, T. Kim, Higher recurrences for Apostol-Bernoulli-Euler numbers, Russ. J. Math. Phys., 19 (2012), 1-10
##[2]
A. Bayad, T. Kim, Identities for Apostol-type Frobenius-Euler polynomials resulting from the study of a nonlinear operator, Russ. J. Math. Phys., 23 (2016), 164-171
##[3]
M. Can, M. Cenkci, V. Kurt, Y. Simsek, Twisted Dedekind type sums associated with Barnes’ type multiple Frobenius- Euler l-functions, Adv. Stud. Contemp. Math. (Kyungshang), 18 (2009), 135-160
##[4]
L. Carlitz, Some polynomials related to the Bernoulli and Euler polynomials, Utilitas Math., 19 (1981), 81-127
##[5]
L. Carlitz, J. Levine, Some problems concerning Kummer’s congruences for the Euler numbers and polynomials, Trans. Amer. Math. Soc., 96 (1960), 23-37
##[6]
T.-Y. Kim, On the multiple q-Genocchi and Euler numbers, Russ. J. Math. Phys., 15 (2008), 481-486
##[7]
D. S. Kim, D. V. Dolgy, T.-Y. Kim, Barnes’ multiple Frobenius-Euler and Hermite mixed-type polynomials, J. Comput. Anal. Appl., 21 (2016), 856-870
##[8]
D. S. Kim, T.-Y. Kim, Higher-order Frobenius-Euler and poly-Bernoulli mixed-type polynomials, Adv. Difference Equ., 2013 (2013 ), 1-13
##[9]
D. S. Kim, T.-Y. Kim, S.-H. Lee, S.-H. Rim, A note on the higher-order Frobenius-Euler polynomials and Sheffer sequences, Adv. Difference Equ., 2013 (2013 ), 1-12
##[10]
D. S. Kim, T.-Y. Kim, J.-J. Seo, T. Komatsu, Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials, Adv. Difference Equ., 2014 (2014 ), 1-16
##[11]
T.-Y. Kim, B.-J. Lee, Some identities of the Frobenius-Euler polynomials, Abstr. Appl. Anal., 2009 (2009 ), 1-7
##[12]
T.-K. Kim, J. J. Seo, Some identities involving Frobenius-Euler polynomials and numbers, Proc. Jangjeon Math. Soc., 19 (2016), 39-46
##[13]
K. Shiratani, On Euler numbers, Mem. Fac. Sci. Kyushu Univ. Ser. A, 27 (1973), 1-5
##[14]
K. Shiratani, S. Yamamoto, On a p-adic interpolation function for the Euler numbers and its derivatives, Mem. Fac. Sci. Kyushu Univ. Ser. A, 39 (1985), 113-125
]
Strong convergence of hybrid Bregman projection algorithm for split feasibility and fixed point problems in Banach spaces
Strong convergence of hybrid Bregman projection algorithm for split feasibility and fixed point problems in Banach spaces
en
en
In this paper, we consider and study split feasibility and fixed point problems involved in Bregman quasi-strictly pseudocontractive
mapping in Banach spaces. It is proven that the sequences generated by the proposed iterative algorithm converge
strongly to the common solution of split feasibility and fixed point problems.
192
204
Jin-Zuo
Chen
Department of Mathematics
Shanghai Normal University
China
chanjanegeoger@163.com
Hui-Ying
Hu
Department of Mathematics
Shanghai Normal University
China
huiying1117@hotmail.com
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Split feasibility problem
fixed point problem
Bregman quasi-strictly pseudo-contractive mapping
Bregman projection
strong convergence.
Article.19.pdf
[
[1]
R. P. Agarwal, J.-W. Chen, Y. J. Cho, Strong convergence theorems for equilibrium problems and weak Bregman relatively nonexpansive mappings in Banach spaces, J. Inequal. Appl., 2013 (2013 ), 1-16
##[2]
Y. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York, 178 (1996), 15-50
##[3]
H. H. Bauschke, J. M. Borwein, P. L. Combettes, Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces, Commun. Contemp. Math., 3 (2001), 615-647
##[4]
L. M. Brégman, A relaxation method of finding a common point of convex sets and its application to the solution of problems in convex programming, (Russian) Ž. Vyčisl. Mat. i Mat. Fiz., 7 (1967), 620-631
##[5]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453
##[6]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
##[7]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, An extragradient method for solving split feasibility and fixed point problems, Comput. Math. Appl., 64 (2012), 633-642
##[8]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem, Nonlinear Anal., 75 (2012), 2116-2125
##[9]
L.-C. Ceng, C.-M. Chen, C.-F. Wen, Generalized mixed equilibria, variational inequalities and common fixed point problems, J. Nonlinear Convex Anal., 16 (2015), 2365-2400
##[10]
L.-C. Ceng, C.-F. Wen, Implicit hybrid steepest-descent methods for generalized mixed equilibria with variational inclusions and variational inequalities, J. Nonlinear Convex Anal., 17 (2016), 987-1012
##[11]
L.-C. Ceng, M.-M. Wong, A. Petruşel, J.-C. Yao, Relaxed implicit extragradient-like methods for finding minimum-norm solutions of the split feasibility problem, Fixed Point Theory, 14 (2013), 327-344
##[12]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353-2365
##[13]
Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
##[14]
Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084
##[15]
Y. Censor, A. Motova, A. Segal, Perturbed projections and subgradient projections for the multiple-sets split feasibility problem, J. Math. Anal. Appl., 327 (2007), 1244-1256
##[16]
S. Y. Cho, S. M. Kang, Approximation of viscosity zero points of accretive operators in a Banach space, Filomat, 28 (2014), 2175-2184
##[17]
N.-N. Fang, Y.-P. Gong, Viscosity iterative methods for split variational inclusion problems and fixed point problems of a nonexpansive mapping, Commun. Optim. Theory, 2016 (2016 ), 1-15
##[18]
K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl., 279 (2003), 372-379
##[19]
X.-L. Qin, S. Y. Cho, L. Wang, Algorithms for treating equilibrium and fixed point problems, Fixed Point Theory Appl., 2013 (2013 ), 1-15
##[20]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016 ), 1-9
##[21]
F. Schöpfer, T. Schuster, A. K. Louis, An iterative regularization method for the solution of the split feasibility problem in Banach spaces, Inverse Problems, 24 (2008), 1-20
##[22]
W. Takahashi, The split feasibility problem in Banach spaces, J. Nonlinear Convex Anal., 15 (2014), 1349-1355
##[23]
G. C. Ugwunnadi, B. Ali, I. Idris, S. M. Minjibir, Strong convergence theorem for quasi-Bregman strictly pseudocontractive mappings and equilibrium problems in Banach spaces, Fixed Point Theory Appl., 2014 (2014 ), 1-16
##[24]
F.-H. Wang, A new algorithm for solving the multiple-sets split feasibility problem in Banach spaces, Numer. Funct. Anal. Optim., 35 (2014), 99-110
##[25]
Z.-M. Wang, Strong convergence theorems for Bregman quasi-strict pseudo-contractions in reflexive Banach spaces with applications, Fixed Point Theory Appl., 2015 (2015 ), 1-17
##[26]
Y.-H. Yao, G. Marino, L. Muglia, A modified Korpelevich’s method convergent to the minimum-norm solution of a variational inequality, Optimization, 63 (2014), 559-569
##[27]
Y.-H. Yao, G. Marino, H.-K. Xu, Y.-C. Liou, Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces, J. Inequal. Appl., 2014 (2014), 1-14
##[28]
Y.-H. Yao, M. Postolache, S. M. Kang, Strong convergence of approximated iterations for asymptotically pseudocontractive mappings, Fixed Point Theory Appl., 2014 (2014 ), 1-13
]
Hermite--Hadamard type inequalities for (\(\alpha,m\))-HA and strongly (\(\alpha,m\))-HA convex functions
Hermite--Hadamard type inequalities for (\(\alpha,m\))-HA and strongly (\(\alpha,m\))-HA convex functions
en
en
In the paper, the authors define the concepts of (\(\alpha,m\))-harmonic-arithmetically convex functions and strongly (\(\alpha,m\))-
harmonic-arithmetically convex functions, establish a new integral identity, and present some new Hermite–Hadamard type
inequalities for (\(\alpha,m\))-harmonic-arithmetically convex functions and strongly (\(\alpha,m\))-harmonic-arithmetically convex functions.
205
214
Chun-Ying
He
College of Mathematics
Inner Mongolia University for Nationalities
China
hechunying9209@qq.com
Yan
Wang
College of Mathematics
Inner Mongolia University for Nationalities
China
sella110@vip.qq.com
Bo-Yan
Xi
College of Mathematics
Inner Mongolia University for Nationalities
China
baoyintu78@qq.com
Feng
Qi
Department of Mathematics, College of Science,
Institute of Mathematics
Tianjin Polytechnic University
Henan Polytechnic University
China
China
qifeng618@gmail.com;qifeng618@hotmail.com
Strongly (\(\alpha،m\))-harmonic-arithmetically convex function
(\(\alpha،m\))-harmonic-arithmetically convex function
integral identity
Hermite–Hadamard type integral inequality.
Article.20.pdf
[
[1]
R.-F. Bai, F. Qi, B.-Y. Xi, Hermite-Hadamard type inequalities for the m- and ((\alpha,m\))-logarithmically convex functions, Filomat, 27 (2013), 1-7
##[2]
S. S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math., 33 (2002), 55-65
##[3]
S. S. Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95
##[4]
S. S. Dragomir, G. Toader, Some inequalities for m-convex functions, Studia Univ. Babe-Bolyai Math., 38 (1993), 21-28
##[5]
J. Hua, B.-Y. Xi, F. Qi, Inequalities of Hermite-Hadamard type involving an s-convex function with applications, Appl. Math. Comput., 246 (2014), 752-760
##[6]
U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147 (2004), 137-146
##[7]
M. Klaričić Bakula, M. E. Özdemir, J. Pečarić, Hadamard type inequalities for m-convex and ((\alpha,m\))-convex functions, JIPAM. J. Inequal. Pure Appl. Math., 9 (2008), 1-12
##[8]
V. G. Miheşan, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj- Napoca, Romania (1993)
##[9]
M. A. Noor , Advanced Convex Analysis, Lecture Notes, Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan (2010)
##[10]
M. A. Noor, K. I. Noor, S. Iftikhar, Hermite-Hadamard inequalities for strongly harmonic convex functions, J. Inequal. Spec. Funct., 7 (2016), 99-113
##[11]
C. E. M. Pearce, J. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formul, Appl. Math. Lett., 13 (2000), 51-55
##[12]
B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl., 7 (1966), 72-75
##[13]
F. Qi, B.-Y. Xi, Some Hermite-Hadamard type inequalities for geometrically quasi-convex functions, Proc. Indian Acad. Sci. Math. Sci., 124 (2014), 333-342
##[14]
F. Qi, T.-Y. Zhang, B.-Y. Xi, Hermite-Hadamard-type integral inequalities for functions whose first derivatives are convex, Reprint of Ukraïn. Mat. Zh., 67 (2015), 555–567, Ukrainian Math. J., 67 (2015), 625-640
##[15]
G. Toader, Some generalizations of the convexity, Proceedings of the colloquium on approximation and optimization,/ Cluj-Napoca, (1985), 329–338, Univ. Cluj-Napoca, Cluj-Napoca (1985)
##[16]
B.-Y. Xi, R.-F. Bai, F. Qi, Hermite-Hadamard type inequalities for the m- and ((\alpha,m\))-geometrically convex functions, Aequationes Math., 84 (2012), 261-269
##[17]
B.-Y. Xi, F. Qi, Hermite-Hadamard type inequalities for geometrically r-convex functions, Studia Sci. Math. Hungar., 51 (2014), 530-546
##[18]
B.-Y. Xi, F. Qi, Inequalities of Hermite-Hadamard type for extended s-convex functions and applications to means, J. Nonlinear Convex Anal., 16 (2015), 873-890
##[19]
B.-Y. Xi, S.-H. Wang, F. Qi, Some inequalities for (h,m)-convex functions, J. Inequal. Appl., 2014 (2014 ), 1-12
##[20]
B.-Y. Xi, T.-Y. Zhang, F. Qi, Some inequalities of Hermite-Hadamard type for m-harmonic-arithmetically convex functions, ScienceAsia, 41 (2015), 357-361
]
Stochastic maximum principle for delayed backward doubly stochastic control systems
Stochastic maximum principle for delayed backward doubly stochastic control systems
en
en
In this paper, we investigate a class of doubly stochastic optimal control problems that the state trajectory is described
by backward doubly stochastic differential equations with time delay. By means of martingale representation theorem and
contraction mapping principle, the existence and uniqueness of solution for the delayed backward doubly stochastic differential
equation can be guaranteed. When the control domain is convex, we deduce a stochastic maximum principle as a necessary
condition of the optimal control by using classical variational technique. At the same time, under certain assumptions, a sufficient
condition of optimality is obtained by using the duality method. In the last section, we give the explicit form of the optimal
control for delayed doubly stochastic linear quadratic optimal control problem by our stochastic maximal principle.
215
226
Jie
Xu
School of Mathematics
College of Sciences
Jilin University
Jilin Institute of Chemical Technology
China
China
aqie990132@126.com
Yuecai
Han
School of Mathematics
Jilin University
China
hanyc@jlu.edu.cn
Stochastic maximum principle
doubly stochastic differential equation
time delay
optimal control.
Article.21.pdf
[
[1]
L. Chen, J.-H. Huang, Stochastic maximum principle for controlled backward delayed system via advanced stochastic differential equation, J. Optim. Theory Appl., 167 (2015), 1112-1135
##[2]
L. Chen, Z. Wu, Maximum principle for the stochastic optimal control problem with delay and application, Automatica J. IFAC, 46 (2010), 1074-1080
##[3]
M. Hafayed, Singular mean-field optimal control for forward-backward stochastic systems and applications to finance, Int. J. Dyn. Control, 2 (2014), 542-554
##[4]
M. Hafayed, M. Ghebouli, S. Boukaf, Partial information optimal control of mean-field forwardbackward stochastic system driven by Teugels martingales with applications, Neurocomputing, 200 (2016), 11-21
##[5]
M. Hafayed, M. Tabet, S. Boukaf, Mean-field maximum principle for optimal control of forward-backward stochastic systems with jumps and its application to mean-variance portfolio problem, Commun. Math. Stat., 3 (2015), 163-186
##[6]
Y.-C. Han, S.-G. Peng, Z. Wu, Maximum principle for backward doubly stochastic control systems with applications, SIAM J. Control Optim., 48 (2010), 4224-4241
##[7]
J.-H. Huang, X. Li, J.-T. Shi, Forward-backward linear quadratic stochastic optimal control problem with delay, Systems Control Lett., 61 (2012), 623-630
##[8]
Q. Lin, A generalized existence theorem of backward doubly stochastic differential equations, Acta Math. Sin. (Engl. Ser.), 26 (2010), 1525-1534
##[9]
A. Matoussi, M. Scheutzow, Stochastic PDEs driven by nonlinear noise and backward doubly SDEs, J. Theoret. Probab., 15 (2002), 1-39
##[10]
D. Nualart, E. Pardoux , Stochastic calculus with anticipating integrands, Probab. Theory Related Fields, 78 (1988), 535-581
##[11]
É. Pardoux, S.-G. Peng, Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Related Fields, 98 (1994), 209-227
##[12]
S.-G. Peng, Y.-F. Shi, A type of time-symmetric forward-backward stochastic differential equations, C. R. Math. Acad. Sci. Paris, 336 (2003), 773-778
##[13]
S.-G. Peng, Z. Yang, Anticipated backward stochastic differential equations, Ann. Probab., 37 (2009), 877-902
##[14]
D. Revuz, M. Yor, Continuous martingales and Brownian motion , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (1991)
##[15]
Y.-F. Shi, Y.-L. Gu, K. Liu, Comparison theorems of backward doubly stochastic differential equations and applications, Stoch. Anal. Appl., 23 (2005), 97-110
##[16]
S. Wu, G.-C. Wang, Optimal control problem of backward stochastic differential delay equation under partial information, Systems Control Lett., 82 (2015), 71-78
##[17]
X.-M. Xu, Anticipated backward doubly stochastic differential equations, Appl. Math. Comput., 220 (2013), 53-62
##[18]
J.-M. Yong, Optimality variational principle for controlled forward-backward stochastic differential equations with mixed initial-terminal conditions, SIAM J. Control Optim., 48 (2010), 4119-4156
##[19]
F. Zhang, Anticipated backward doubly stochastic differential equations, (Chinese) J. Sci. Sin. Math., 43 (2013), 1223-1236
]
On completeness of root vectors of Schrödinger operators: a spectral approach
On completeness of root vectors of Schrödinger operators: a spectral approach
en
en
We study complete properties of root vectors of Schrödinger operators. More accurately, denote by \(B(r_0)\) be the ball
centered at the origin with radius \(r_0\) and \(L^1(B(r_0))\) the space which consists of real functions f(x) satisfying
\(\int_{B(r_0)}|f(x)|dx<\infty\),
then the complete properties of eigenvectors for Schrödinger equation are characterized. Our characterization depends on the
sum of eigenvalues. Our proof is based on a complex-analytic conjugate approach which is widely used in the investigation of
completeness of function systems in Banach spaces.
227
233
Xiangdong
Yang
Department of Mathematics
KunMing University of Science and Technology
China
yangsddp@126.com
Schrödinger operators
inverse eigenvalue problem
completeness.
Article.22.pdf
[
[1]
R. P. Boas, Jr., Entire functions, Academic Press Inc., New York (1954)
##[2]
A. Boivin, H.-L. Zhong, Completeness of systems of complex exponentials and the Lambert W functions, Trans. Amer. Math. Soc., 359 (2007), 1829-1849
##[3]
T. Bouhennache, Point spectrum of elliptic operators in fibered half-cylinders and the related completeness problem, Integral Equations Operator Theory, 39 (2001), 182-192
##[4]
N. Dunford, J. Schwartz, Linear operators, Part I, General theory, With the assistance of William G. Bade and Robert G. Bartle, Reprint of the 1958 original. Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York (1988)
##[5]
R. L. Frank, A. Laptev, E. H. Lieb, R. Seiringer, Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials, Lett. Math. Phys., 77 (2006), 309-316
##[6]
J. B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London (1981)
##[7]
F. Gesztesy, V. Tkachenko, A Schauder and Riesz basis criterion for non-self-adjoint Schrödinger operators with periodic and antiperiodic boundary conditions, J. Differential Equations, 253 (2012), 400-437
##[8]
S. A. Guda, Completeness of the Floquet solutions to the problem of a solid oscillating in a fluid, Sib. Math. J., 50 (2009), 405-414
##[9]
V. Isakov , Completeness of products of solutions and some inverse problems for PDE, J. Differential Equations, 92 (1991), 305-316
##[10]
L. Knockaert, D. D. Zutter, On the completeness of eigenmodes in a parallel plate waveguide with a perfectly matched layer termination, IEEE Trans. Antennas. Propag., 50 (2002), 1650-1653
##[11]
A. Laptev, O. Safronov, Eigenvalue estimates for Schrödinger operators with complex potentials, Comm. Math. Phys., 292 (2009), 29-54
##[12]
G. V. Radzıevksiĭ, Multiple completeness of the root vectors of an M. V. Keldyš pencil that is perturbed by an operator-valued function analytic in the disc, (Russian) Mat. Sb. (N.S.), 91 (1973), 310-335
##[13]
A. G. Ramm, Completeness of the products of solutions to PDE and uniqueness theorems in inverse scattering, Inverse Problems, 3 (1987), 77-82
##[14]
A. G. Ramm, An inverse scattering problem with part of the fixed-energy phase shifts, Comm. Math. Phys., 207 (1999), 231-247
##[15]
A. G. Ramm, Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave, J. Math. Phys., 52 (2011), 1-12
##[16]
Z. Wang, H.-Y. Wu, The completeness of eigenfunctions of perturbation connected with Sturm-Liouville operators, J. Syst. Sci. Complex., 19 (2006), 527-537
##[17]
Y. Yakubov, Completeness of elementary solutions of second order elliptic equations in a semi-infinite tube domain, Electron. J. Differential Equations, 2002 (2002), 1-21
##[18]
X.-D. Yang, Incompleteness of exponential system in the weighted Banach space, J. Approx. Theory, 153 (2008), 73-79
##[19]
X.-D. Yang, Random inverse spectral problems and closed random exponential systems, Inverse Problems, 30 (2014), 1-12
##[20]
X.-D. Yang, J. Tu, On the completeness of the system \(\{t^{\lambda_n}\}\) in \(C_0(E)\), J. Math. Anal. Appl., 368 (2010), 429-437
]
The approximation of solutions for second order nonlinear oscillators using the polynomial least square method
The approximation of solutions for second order nonlinear oscillators using the polynomial least square method
en
en
In this paper, polynomial least square method (PLSM) is applied to find approximate solution for nonlinear oscillator
differential equations. We illustrate that this method is very convenient and does not require linearization or small parameters.
Comparisons are made between the results of PLSM and other methods in order to prove the accuracy of the PLSM method.
234
242
Constantin
Bota
Dept. of Mathematics
Politehnica” University of Timişoara
Romania
costelbota@yahoo.com
Nonlinear oscillators
approximate polynomial solution.
Article.23.pdf
[
[1]
A. Barari, M. Omidvar, A. R. Ghotbi, D. D. Ganji, Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations, Acta Appl. Math., 104 (2008), 161-171
##[2]
A. Beléndez, E. Gimeno, T. Beléndez, A. Hernández , Rational harmonic balance based method for conservative nonlinear oscillators: application to the Duffing equation, Mech. Res. Comm., 36 (2009), 728-734
##[3]
A. Beléndez, A. Hernandez, T. Beléndez, M. L. Alvarez, S. Gallego, M. Ortuño, C. Neipp, Application of the harmonic balance method to a nonlinear oscillator typified by a mass attached to a stretched wire, J. Sound Vib., 302 (2007), 1018-1029
##[4]
S. Durmaz, S. Altay Demirbağ, M. O. Kaya, Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire, Comput. Math. Appl., 61 (2011), 578-585
##[5]
Y.-M. Fu, J. Zhang, L.-J. Wan, Application of the energy balance method to a nonlinear oscillator arising in the microelectromechanical system (MEMS), Curr. Appl. Phys., 11 (2011), 482-485
##[6]
S. S. Ganji, D. D. Ganji, M. G. Sfahani, S. Karimpour, Application of AFF and HPM to the systems of strongly nonlinear oscillation, Curr. Appl. Phys., 10 (2010), 1317-1325
##[7]
D. D. Ganji, M. Gorji, S. Soleimani, M. Esmaeilpour, Solution of nonlinear cubic-quintic Duffing oscillators using He’s Energy Balance Method, J. Zhejiang Univ. Sci. A , 10 (2009), 1263-1268
##[8]
F. Geng, A piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire, Comput. Math. Appl., 62 (2011), 1641-1644
##[9]
S. Ghosh, A. Roy, D. Roy, An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators, Comput. Methods Appl. Mech. Engrg., 196 (2007), 1133-1153
##[10]
A. Golbabai, M. Fardi, K. Sayevand, Application of the optimal homotopy asymptotic method for solving a strongly nonlinear oscillatory system, Math. Comput. Modelling, 58 (2013), 1837-1843
##[11]
M. N. Hamdan, N. H. Shabaneh, On the large amplitude free vibrations of a restrained uniform beam carrying an intermediate lumped mass, J. Sound Vib., 199 (1997), 711-736
##[12]
J.-H. He, The homotopy perturbation method nonlinear oscillators with discontinuities, Appl. Math. Comput., 151 (2004), 287-292
##[13]
J.-H. He, Variational approach for nonlinear oscillators, Chaos Solitons Fractals, 34 (2007), 1430-1439
##[14]
N. Jamshidi, D. D. Ganji, Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire, Curr. Appl. Phys., 10 (2010), 484-48
##[15]
H. Kaur, R. C. Mittal, V. Mishra, Haar wavelet solutions of nonlinear oscillator equations, Appl. Math. Model., 38 (2014), 4958-4971
##[16]
Y. Khan, M. Akbarzade, A. Kargar, Coupling of homotopy and the variational approach for a conservative oscillator with strong odd-nonlinearity, Sci. Iran., 19 (2012), 417-422
##[17]
I. Kovacic, M. J. Brennan (Ed.), The Duffing equation, Nonlinear oscillators and their behaviour, John Wiley & Sons, Ltd., Chichester (2011)
##[18]
V. Marinca, N. Herişanu, Periodic solutions of Duffing equation with strong non-linearity, Chaos Solitons Fractals, 37 (2008), 144-149
##[19]
Y.-H. Qian, S.-K. Lai, W. Zhang, Y. Xiang, Study on asymptotic analytical solutions using HAM for strongly nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass, Numer. Algorithms, 58 (2011), 293-314
##[20]
M. Razzaghi, G. Elnagar, Numerical solution of the controlled Duffing oscillator by the pseudospectral method, J. Comput. Appl. Math., 56 (1994), 253-261
##[21]
S. Tellı, O. Kopmaz, Free vibrations of a mass grounded by linear and nonlinear springs in series, J. Sound Vib., 289 (2006), 689-710
##[22]
L. Xu, Application of He’s parameter-expansion method to an oscillation of a mass attached to a stretched elastic wire, Phys. Lett. A, 368 (2007), 259-262
]
Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions
Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions
en
en
In this paper, we study the existence and uniqueness of positive solutions for a class of singular fractional differential
systems with coupled integral boundary conditions. By using the properties of the Green function, the mixed monotone method
and the fixed point theory in cones, we obtain the existence and uniqueness results for the problem. The results obtained herein
generalize and improve some known results including singular and non-singular cases.
243
262
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University
China
Australia
mathlls@163.com
Hongdan
Li
School of Mathematical Sciences
Qufu Normal University
China
lhd200908@163.com
Chun
Liu
School of Mathematical Sciences
Qufu Normal University
China
liuchunjn@aliyun.com
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University
Australia
yhwu@maths.curtin.edu.au
Singular fractional differential equations
Riemann-Stieltjes integral boundary value problem
positive solution
fixed point theorem in cone.
Article.24.pdf
[
[1]
B. Ahmad, J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl., 58 (2009), 1838-1843
##[2]
C.-Z. Bai, J.-X. Fang, The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations, Appl. Math. Comput., 150 (2004), 611-621
##[3]
Y.-J. Cui, L.-S. Liu, X.-U. Zhang, Uniqueness and existence of positive solutions for singular differential systems with coupled integral boundary value problems, Abstr. Appl. Anal., 2013 (2013), 1-9
##[4]
W.-Q. Feng, S.-R. Sun, Z.-L. Han, Y.-G. Zhao, Existence of solutions for a singular system of nonlinear fractional differential equations, Comput. Math. Appl., 62 (2011), 1370-1378
##[5]
D.-J. Guo, V. Lakshmikantham, Nonlinear problems in abstract cones, Notes and Reports in Mathematics in Science and Engineering, Academic Press, Inc., Boston, MA (1988)
##[6]
L.-M. Guo, L.-S. Liu, Y.-H. Wu, Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions, Bound. Value Probl., 2016 (2016 ), 1-20
##[7]
J. Henderson, R. Luca, Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems, NoDEA Nonlinear Differential Equations Appl., 20 (2013), 1035-1054
##[8]
J. Henderson, R. Luca, Existence and multiplicity of positive solutions for a system of fractional boundary value problems, Bound. Value Probl., 2014 (2014 ), 1-17
##[9]
J. J. Jiang, L.-S. Liu, Existence of solutions for a sequential fractional differential system with coupled boundary conditions, Bound. Value Probl., 2016 (2016 ), 1-15
##[10]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., (2006), -
##[11]
W.-W. Liu, L.-S. Liu, Y.-H. Wu, Positive solutions of a singular boundary value problem for systems of second-order differential equations, Appl. Math. Comput., 208 (2009), 511-519
##[12]
L. Liu, F. Sun, X. Zhang, Y. Wu, Bifurcation analysis for a singular differential system with two parameters via to degree theory, Nonlinear Anal. MC, 22 (2017), 31-50
##[13]
S.-Y. Liu, G.-T. Wang, L.-H. Zhang, Existence results for a coupled system of nonlinear neutral fractional differential equations, Appl. Math. Lett., 26 (2013), 1120-1124
##[14]
A. Lomtatidze, L. Malaguti, On a nonlocal boundary value problem for second order nonlinear singular differential equations, Georgian Math. J., 7 (2000), 133-154
##[15]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[16]
H. A. H. Salem, On the existence of continuous solutions for a singular system of non-linear fractional differential equations, Appl. Math. Comput., 198 (2008), 445-452
##[17]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Theory and applications, Edited and with a foreword by S. M. Nikolski˘ı, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon (1993)
##[18]
X.-W. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett., 22 (2009), 64-69
##[19]
F.-L. Sun, L.-S. Liu, X.-U. Zhang, Y.-H. Wu, Spectral analysis for a singular differential system with integral boundary conditions, Mediterr. J. Math., 13 (2016), 4763-4782
##[20]
M. ur Rehman, R. Ali Khan, A note on boundary value problems for a coupled system of fractional differential equations, Comput. Math. Appl., 61 (2011), 2630-2637
##[21]
Y. Wang, L.-S. Liu, X.-U. Zhang, Y.-H. Wu, Positive solutions for (n - 1, 1)-type singular fractional differential system with coupled integral boundary conditions, Abstr. Appl. Anal., 2014 (2014 ), 1-14
##[22]
Y. Wang, L.-S. Liu, X.-U. Zhang, Y.-H. Wu , Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection, Appl. Math. Comput., 258 (2015), 312-324
##[23]
W.-G. Yang, Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions, Comput. Math. Appl., 63 (2012), 288-297
##[24]
C.-J. Yuan, Multiple positive solutions for (n - 1, 1)-type semipositone conjugate boundary value problems of nonlinear fractional differential equations, Electron. J. Qual. Theory Differ. Equ., 2010 (2010 ), 1-12
##[25]
C.-J. Yuan, Two positive solutions for (n - 1, 1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 930-942
]
A modified iterative algorithm for finding a common element in Hilbert space
A modified iterative algorithm for finding a common element in Hilbert space
en
en
In this paper, a modified iterative algorithm for finding a common element of the solutions of a equilibrium problem, the
set of fixed points of nonexpansive mappings and the set of solutions of variational inequality problem is constructed in Hilbert
spaces, and the strong convergence of the generated iterative sequence to the common element is proved under some mild
conditions. The main result proposed in this paper extends and improves some recent results in the literature.
263
277
Zhichuan
Zhu
School of Statistics
School of Mathematics and Statistics
Jilin University of Finance and Economics
Northeast Normal University
China
China
zhuzcnh@126.com
Yanchun
Xing
School of Statistics
School of Mathematics and Statistics
Jilin University of Finance and Economics
Northeast Normal University
China
China
xingyanchun778@163.com
Weihua
Duan
Yatai School of Business Administration
Jilin University of Finance and Economics
China
duanweihua@jlufe.edu.cn
Common element
iterative algorithm
Hilbert space
strong convergence.
Article.25.pdf
[
[1]
E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145
##[2]
A. Bnouhachem, A modified projection method for a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixed-point problem, Fixed Point Theory Appl., 2014 (2014 ), 1-25
##[3]
L.-C. Ceng, A. Latif, A. E. Al-Mazrooei, Hybrid viscosity methods for equilibrium problems, variational inequalities, and fixed point problems, Appl. Anal., 95 (2016), 1088-1117
##[4]
P. L. Combettes, S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., 6 (2005), 117-136
##[5]
Q.-W. Fan, W. Wu, J. M. Zurada, Convergence of batch gradient learning with smoothing regularization and adaptive momentum for neural networks, SpringerPlus, 5 (2016), 1-17
##[6]
H.-M. He, S.-Y. Liu, R.-D. Chen, Convergence results of multi-valued nonexpansive mappings in Banach spaces, J. Inequal. Appl., 2014 (2014), 1-12
##[7]
H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal., 61 (2005), 341-350
##[8]
G. Marino, H.-K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 318 (2006), 43-52
##[9]
H. Piri , A general iterative method for finding common solutions of system of equilibrium problems, system of variational inequalities and fixed point problems, Math. Comput. Modelling, 55 (2012), 1622-1638
##[10]
S. Plubtieng, R. Punpaeng, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 336 (2007), 445-469
##[11]
R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 149 (1970), 75-88
##[12]
Y.-S. Song, K. Promluang, P. Kumam, Y. J. Cho, Some convergence theorems of the Mann iteration for monotone \(\alpha\)- nonexpansive mappings, Appl. Math. Comput., 287/288 (2016), 74-82
##[13]
T. Suzuki, Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl., 305 (2005), 227-239
##[14]
S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 331 (2007), 506-515
##[15]
W. Takahashi, M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., 118 (2003), 417-428
##[16]
Y.-H. Yao, Y. J. Cho, R.-D. Chen, An iterative algorithm for solving fixed point problems, variational inequality problems and mixed equilibrium problems, Nonlinear Anal., 71 (2009), 3363-3373
##[17]
Y.-H. Yao, J.-C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., 186 (2007), 1551-1558
##[18]
Z.-C. Zhu, R.-D. Chen, Strong convergence on iterative methods of Cesro means for nonexpansive mapping in Banach space, Abstr. Appl. Anal., 2014 (2014 ), 1-6
##[19]
Z.-C. Zhu, B. Yu, A modified homotopy method for solving the principal-agent bilevel programming problem, Comput. Appl. Math., 2016 (2016), 1-26
##[20]
Z.-C. Zhu, B. Yu, Globally convergent homotopy algorithm for solving the KKT systems to the principal-agent bilevel programming, Optim. Methods Softw., 32 (2017), 69-85
##[21]
Z.-C. Zhu, B. Yu, Y.-F. Shang, A modified homotopy method for solving nonconvex fixed points problems, Fixed Point Theory, 14 (2013), 531-544
##[22]
Z.-C. Zhu, B. Yu, L. Yang, Globally convergent homotopy method for designing piecewise linear deterministic contractual function, J. Ind. Manag. Optim., 10 (2014), 717-741
]
Application of the double Laplace Adomian decomposition method for solving linear singular one dimensional thermo-elasticity coupled system
Application of the double Laplace Adomian decomposition method for solving linear singular one dimensional thermo-elasticity coupled system
en
en
In the present work, the Adomain decomposition and double Laplace transform methods are combined to solve linear
singular one dimensional hyperbolic equation and linear singular one dimensional thermo-elasticity coupled system. Also we
address the convergence of double Laplace transform decomposition method. Moreover, some examples are given to establish
our method.
278
289
Hassan
Eltayeb
Mathematics Department, College of Science
King Saud University
Saudi Arabia
hgadain@ksu.edu.sa
Adem
Kilicman
Department of Mathematics
University Putra Malaysia
Malaysia
akilic@upm.edu.my
Said
Mesloub
Mathematics Department, College of Science
King Saud University
Saudi Arabia
mesloub@ksu.edu.sa
Double Laplace transform
inverse Laplace transform
nonlinear hyperbolic equation
single Laplace transform
decomposition methods
thermo-elasticity.
Article.26.pdf
[
[1]
K. Abbaoui, Y. Cherruault, Convergence of Adomian’s method applied to differential equations, Comput. Math. Appl., 28 (1994), 103-109
##[2]
K. Abbaoui, Y. Cherruault, Convergence of Adomian’s method applied to nonlinear equations, Math. Comput. Modelling, 20 (1994), 69-73
##[3]
K. Abbaoui, Y. Cherruault, V. Seng, Practical formulae for the calculus of multivariable Adomian polynomials, Math. Comput. Modelling, 22 (1995), 89-93
##[4]
S. Abbasbandy, Iterated He’s homotopy perturbation method for quadratic Riccati differential equation, Appl. Math. Comput., 175 (2006), 581-589
##[5]
A. Atangana, S. C. Oukouomi Noutchie, On multi-Laplace transform for solving nonlinear partial differential equations with mixed derivatives, Math. Probl. Eng., 2014 (2014), 1-9
##[6]
E. Babolian, J. Biazar, A. R. Vahidi, A new computational method for Laplace transforms by decomposition method, Appl. Math. Comput., 150 (2004), 841-846
##[7]
A. Bouziani, On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator, J. Appl. Math., 2003 (2003), 487-502
##[8]
C. A. de Moura, A linear uncoupling numerical scheme for the nonlinear coupled thermoelastodynamics equations, Numerical methods, Caracas, (1982), 204–211, Lecture Notes in Math., Springer, Berlin-New York (1983)
##[9]
H. Eltayeb, A. Kılıçman, A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform, Appl. Math. Lett., 21 (2008), 1324-1329
##[10]
I. Hashim, M. S. M. Noorani, M. R. Said Al-Hadidi, Solving the generalized Burgers-Huxley equation using the Adomian decomposition method, Math. Comput. Modelling, 43 (2006), 1404-1411
##[11]
D. Kaya, I. E. Inan, A convergence analysis of the ADM and an application, Appl. Math. Comput., 161 (2005), 1015-1025
##[12]
D. Kaya, I. E. Inan, A numerical application of the decomposition method for the combined KdV–MKdV equation, Appl. Math. Comput., 168 (2005), 915-926
##[13]
Y. Khan, H. Vázquez-Leal, N. Faraz, An auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations, Appl. Math. Model., 37 (2013), 2702-2708
##[14]
A. Kılıçman, H. Eltayeb, A note on defining singular integral as distribution and partial differential equations with convolution term, Math. Comput. Modelling, 49 (2009), 327-336
##[15]
A. Kılıçman, H. E. Gadain, On the applications of Laplace and Sumudu transforms, J. Franklin Inst., 347 (2010), 848-862
##[16]
T. Mavoungou, Y. Cherruault, Convergence of Adomian’s method and applications to non-linear partial differential equations, Kybernetes, 21 (1992), 13-25
##[17]
T. Mavoungou, Y. Cherruault, Numerical study of Fisher’s equation by Adomian’s method, Math. Comput. Modelling, 19 (1994), 89-95
##[18]
S. Meslouba, F. Mesloub, On a coupled nonlinear singular thermoelastic system, Nonlinear Anal., 73 (2010), 3195-3208
##[19]
A. Sadighi, D. D. Ganji, Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods, Int. J. Nonlinear Sci. Numer. Simul., 8 (2007), 435-443
]
The distributional Henstock-Kurzweil integral and applications II
The distributional Henstock-Kurzweil integral and applications II
en
en
In this paper, we study a special Banach lattice \(D_{HK}\), which is induced by the distributional Henstock-Kurzweil integral,
and discuss its lattice properties. We show that \(D_{HK}\) is an AM-space with the Archimedean property and the Dunford-Pettis
property but it is not Dedekind complete. We also present two fixed point theorems in \(D_{HK}\). Meanwhile, two examples are
worked out to demonstrate the results.
290
298
Wei
Liu
College of Science
Hohai University
P. R. China
liuw626@hhu.edu.cn
Guoju
Ye
College of Science
Hohai University
P. R. China
yegj@hhu.edu.cn
Dafang
Zhao
College of Science
School of Mathematics and Statistics
Hohai University
Hubei Normal University
P. R. China.
P. R. China
dafangzhao@163.com
Distributional Henstock-Kurzweil integral
Banach lattice
AM-space
Archimedean property
Dunford-Pettis property
order continuity
Article.27.pdf
[
[1]
C. D. Aliprantis, K. C. Border, Infinite dimensional analysis, A hitchhiker’s guide, Third edition, Springer, Berlin (2006)
##[2]
C. D. Aliprantis, O. Burkinshaw, Dunford-Pettis operators on Banach lattices, Trans. Amer. Math. Soc., 274 (1982), 227-238
##[3]
C. D. Aliprantis, O. Burkinshaw, Positive operators , Pure and Applied Mathematics, Academic Press, Inc., Orlando, FL (1985)
##[4]
A. Ben Amar, Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock- Kurzweil-Pettis integrability, Comment. Math. Univ. Carolin., 52 , 177–190. (2011)
##[5]
B. Bongiorno, Relatively weakly compact sets in the Denjoy space, The collection of theses of Symposium on Real Analysis, Xiamen, (1993), J. Math. Study, 27 (1994), 37-44
##[6]
D. Bugajewski, On the Volterra integral equation and the Henstock-Kurzweil integral, Math. Pannon., 9 (1998), 141-145
##[7]
T. S. Chew, On Kurzweil generalized ordinary differential equations, J. Differential Equations, 76 (1988), 286-293
##[8]
T. S. Chew, F. Flordeliza, On \(\acute{x}=f(t, x)\) and Henstock-Kurzweil integrals, Differential Integral Equations, 4 (1991), 861-868
##[9]
M. Federson, R. Bianconi, Linear integral equations of Volterra concerning Henstock integrals, Real Anal. Exchange, 25 (1999/00), 389-417
##[10]
M. Federson, R. Bianconi, Linear Volterra-Stieltjes integral equations in the sense of the Kurzweil-Henstock integral, Arch. Math. (Brno), 37 (2001), 307-328
##[11]
D.-J. Guo, Y. J. Cho, J. Zhu, Partial ordering methods in nonlinear problems, Nova Science Publishers, Inc., Hauppauge, NY (2004)
##[12]
J. Kurzweil, Henstock-Kurzweil integration: its relation to topological vector spaces, Series in Real Analysis, World Scientific Publishing Co., Inc., River Edge, NJ (2000)
##[13]
J. Kurzweil, Integration between the Lebesgue integral and the Henstock-Kurzweil integral, Its relation to local convex vector spaces, Series in Real Analysis, World Scientific Publishing Co., Inc., River Edge, NJ (2002)
##[14]
P. Y. Lee, Lanzhou lectures on Henstock integration, Series in Real Analysis, World Scientific Publishing Co., Inc., Teaneck, NJ (1989)
##[15]
P. Y. Lee, R. Výborný, Integral: an easy approach after Kurzweil and Henstock, Australian Mathematical Society Lecture Series, Cambridge University Press, Cambridge (2000)
##[16]
D. O’Regan, Fixed-point theory for weakly sequentially continuous mappings, Math. Comput. Modelling, 27 (1998), 1-14
##[17]
B. Satco, Volterra integral inclusions via Henstock-Kurzweil-Pettis integral, Discuss. Math. Differ. Incl. Control Optim., 26 (2006), 87-101
##[18]
B. R. Satco , Nonlinear Volterra integral equations in Henstock integrability setting, Electron. J. Differential Equations, 2008 (2008), 1-9
##[19]
S. Schwabik, G.-J. Ye, Topics in Banach space integration, Series in Real Analysis, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2005)
##[20]
P. M. Soardi , Existence of fixed points of nonexpansive mappings in certain Banach lattices, Proc. Amer. Math. Soc., 73 (1979), 25-29
##[21]
E. Talvila, The distributional Denjoy integral, Real Anal. Exchange, 33 (2008), 51-82
##[22]
G.-J. Ye, W. Liu, The distributional Henstock-Kurzweil integral and applications, Monatsh. Math., 181 (2016), 975-989
]
Solution of fractional oxygen diffusion problem having without singular kernel
Solution of fractional oxygen diffusion problem having without singular kernel
en
en
In the present paper, we use an efficient approach to solve fractional differential equation, oxygen diffusion problem which
is used to describe oxygen absorption in human body. The oxygen diffusion problem is considered in new Caputo derivative
of fractional order in this paper. Using an iterative approach, we derive the solutions of the modified system.
299
307
Badr S.
Alkahtani
Mathematics Department, College of Science
King Saud University
Saudi Arabia
alhaghog@gmail.com
Obaid J.
Algahtani
Mathematics Department, College of Science
King Saud University
Saudi Arabia
obalgahtani@ksu.edu.sa
Ravi Shanker
Dubey
Department of Mathematics
Yagyavalkya Institute of Technology
India
ravimath13@gmail.com
Pranay
Goswami
School of Liberal Studies
Ambedkar University Delhi
India
pranaygoswami83@gmail.com
Oxygen diffusion problem
Caputo-Fabrizio fractional derivative
fractional differential equation
Laplace transform
fixed-point theorem.
Article.28.pdf
[
[1]
A. Atangana, On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation, Appl. Math. Comput., 273 (2016), 948-956
##[2]
A. Atangana, E. Alabaraoye, Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller-Segel equations, Adv. Difference Equ., 2013 (2013 ), 1-14
##[3]
A. Atangana, B. S. T. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, Entropy, 17 (2015), 4439-4453
##[4]
A. Atangana, S. T. A. Badr, Extension of the RLC electrical circuit to fractional derivative without singular kernel, Adv. Mech. Eng., 7 (2015), 1-6
##[5]
F. B. M. Belgacem, Diffusion and drift models for population dispersal from stochastic and continuum views, Int. J. Appl. Math., 5 (2001), 85-106
##[6]
M. Caputo, Linear models of dissipation whose Q is almost frequency independent, II, Reprinted from Geophys, J. R. Astr. Soc., 13 (1967), 529–539, Fract. Calc. Appl. Anal., 11 (2008), 4-14
##[7]
M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 73-85
##[8]
V. B. L. Chaurasia, R. S. Dubey, Analytical solution for the generalized time-fractional telegraph equation, Fract. Differ. Calc., 3 (2013), 21-29
##[9]
V. B. L. Chaurasia, R. S. Dubey, F. B. M. Belgacem, Fractional radial diffusion equation analytical solution via Hankel and Sumudu transforms, Int. J. Math. Eng. Sci. Aero., 3 (2012), 1-10
##[10]
J. Crank, R. S. Gupta, A method for solving moving boundary problems in heat-flow using cubic splines or polynomials, J. Inst. Math. Appl., 10 (1972), 296-304
##[11]
J. Crank, R. S. Gupta, A moving boundary problem arising from the diffusion of oxygen in absorbing tissue, IMA J. Appl. Math., 10 (1972), 19-23
##[12]
R. S. Dubey, B. S. T. Alkahtani, A. Atangana, Analytical solution of space-time fractional Fokker-Planck equation by homotopy perturbation Sumudu transform method, Math. Probl. Eng., 2014 (2015 ), 1-7
##[13]
R. S. Dubey, P. Goswami, F. B. M. Belgacem, Generalized time-fractional telegraph equation analytical solution by Sumudu and Fourier transforms, J. Fract. Calc. Appl., 5 (2014), 52-58
##[14]
V. Gülkaç, Comparative study between two numerical methods for oxygen diffusion problem, Comm. Numer. Methods Engrg., 25 (2009), 855-863
##[15]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[16]
A. I. Liapis, G. G. Lipscomb, O. K. Crosser, E. Tsiroyianni-Liapis, A model of oxygen diffusion in absorbing tissue, Math. Modelling, 3 (1982), 83-92
##[17]
J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 87-92
##[18]
K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York (1993)
##[19]
S. L. Mitchell, An accurate application of the integral method applied to the diffusion of oxygen in absorbing tissue, Appl. Math. Model., 38 (2014), 4396-4408
##[20]
B. Noble, Heat balance methods in melting problems, J. R. Ockendon, W. R. Hodgkins (Eds.), Moving boundary problems in heat flow and diffusion, Clarendon Press, Oxford, (1975), 208-209
##[21]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[22]
W. C. Reynolds, T. A. Dolton, The use of integral methods in transient heat transfer analysis, ASME paper, (1958)
]
Best proximity points of discontinuous operator in partially ordered metric spaces
Best proximity points of discontinuous operator in partially ordered metric spaces
en
en
In this paper we establish best proximity point results for monotone multivalued mappings in partially ordered metric
spaces. We consider three notions of monotonicity of multivalued mappings. The main theorem is obtained by utilizing
property UC and MT-functions. There is no requirement of continuity on the multivalued function which is illustrated with two
supporting examples of the results established in this paper. There are two corollaries. Some existing results are extended to the
domain of partially ordered metric spaces through one of the corollaries.
308
315
B. S.
Choudhury
Department of Mathematics
Indian Institute of Engineering Science and Technology
India
binayak12@yahoo.co.in
M.
Jleli
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
P.
Maity
Department of Mathematics
Indian Institute of Engineering Science and Technology
India
pranati.math@gmail.com
Best proximity point
multivalued cyclic mapping
multivalued approximately monotone increasing mapping
multivalued partly monotone increasing mapping.
Article.29.pdf
[
[1]
A. Abkar, M. Gabeleh, Best proximity points for cyclic mappings in ordered metric spaces, J. Optim. Theory Appl., 150 (2011), 188-193
##[2]
A. Abkar, M. Gabeleh, Generalized cyclic contractions in partially ordered metric spaces, Optim. Lett., 6 (2012), 1819-1830
##[3]
R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116
##[4]
M. A. Al-Thagafi, N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Anal., 70 (2009), 3665-3671
##[5]
B. S. Choudhury, A. Kundu, (\(\psi,\alpha,\beta\))-weak contractions in partially ordered metric spaces, Appl. Math. Lett., 25 (2012), 6-10
##[6]
B. S. Choudhury, P. Maity, Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling, 54 (2011), 73-79
##[7]
B. S. Choudhury, P. Maity, P. Konar, A global optimality result using nonself mappings, Opsearch, 51 (2014), 312-320
##[8]
B. S. Choudhury, P. Maity, N. Metiya, Best proximity point theorems with cyclic mappings in setvalued analysis, Indian J. Math., 57 (2015), 79-102
##[9]
B. S. Choudhury, P. Maity, N. Metiya, Best proximity point results in set-valued analysis, Nonlinear Anal. Model. Control, 21 (2016), 293-305
##[10]
L. Ćirić, Fixed point theorems for multi-valued contractions in complete metric spaces, J. Math. Anal. Appl., 348 (2008), 499-507
##[11]
L. Ćirić, N. Cakić, M. Rajović, J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2008 (2008 ), 1-11
##[12]
M. De la Sen, S. L. Singh, M. E. Gordji, A. Ibeas, R. P. Agarwal, Best proximity and fixed point results for cyclic multivalued mappings under a generalized contractive condition, Fixed Point Theory Appl., 2013 (2013 ), 1-21
##[13]
C. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 69 (2008), 3790-3794
##[14]
W.-S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topology Appl., 159 (2012), 49-56
##[15]
W.-S. Du, H. Lakzian, Nonlinear conditions for the existence of best proximity points, J. Inequa. Appl., 2012 (2012 ), 1-7
##[16]
A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006
##[17]
K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 122 (1969), 234-240
##[18]
M. Jleli, B. Samet , Best proximity point results for MK-proximal contractions on ordered sets, J. Fixed Point Theory Appl., 17 (2015), 439-452
##[19]
E. Karapınar, Best proximity points of cyclic mappings, Appl. Math. Lett., 25 (2012), 1761-1766
##[20]
E. Karapınar, G. Petruşel, K. Tas, Best proximity point theorems for KT-types cyclic orbital contraction mappings, Fixed Point Theory, 13 (2012), 537-546
##[21]
W. A. Kirk, S. Reich, P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim., 24 (2003), 851-862
##[22]
N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), 177-188
##[23]
S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
##[24]
K. Neammanee, A. Kaewkhao, Fixed points and best proximity points for multi-valued mapping satisfying cyclical condition, Int. J. Math. Sci. Appl., 1 (2011), 1-9
##[25]
V. Pragadeeswarar, M. Marudai, Best proximity points: approximation and optimization in partially ordered metric spaces, Optim. Lett., 7 (2013), 1883-1892
##[26]
W. Sintunavarat, P. Kumam, Coupled best proximity point theorem in metric spaces, Fixed Point Theory Appl., 2012 (2012 ), 1-16
##[27]
T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., 71 (2009), 2918-2926
##[28]
M. Turinici , Abstract comparison principles and multivariable Gronwall-Bellman inequalities, J. Math. Anal. Appl., 117 (1986), 100-127
]
Some transcendence properties of integrals of Bessel functions
Some transcendence properties of integrals of Bessel functions
en
en
We prove that some integrals of Bessel functions are transcendence over ring of Bessel functions with coefficients from the
field of rational fractions of one variable.
316
324
Gulsah
Oner
Dokuz Eylul University
Turkey
gulsah.darilmaz@deu.edu.tr
Mikhail V.
Neschadim
Sobolev Institute of Mathematics and Novosibirsk State University
Russia
neshch@math.nsc.ru
Tahsin
Oner
Department of Mathematics
Ege University
Turkey
tahsin.oner@ege.edu.tr
Independence
differential algebra
Bessel functions
transcendence properties.
Article.30.pdf
[
[1]
N. I. Fel’dman, A. B. Shidlovskiĭ , The development and present state of the theory of transcendental numbers, (Russian) Uspehi Mat. Nauk, 22 (1967), 3-81
##[2]
O. Holder, Memoire sur la fonction \(\Gamma\), Math. Annal, (1887), 1-13
##[3]
I. Kaplansky , An introduction to differential algebra, Actualités Sci. Ind., Publ. Inst. Math. Univ. Nancago, Hermann, Paris (1957)
##[4]
E. R. Kolchin , Extensions of differential fields I, II, III., Ann. Math., 43 (1942), 724–729, Ann. Math., 45 (1944), 358–361, BAMS, 53 (1947), 397-401
##[5]
L. Markus, Differential independence of meromorphic functions, University of Minnesota Research Report, (2003), 1-34
##[6]
F. W. J. Olver, Asymptotics and special functions, Computer Science and Applied Mathematics. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1974)
##[7]
J. F. Ritt, Integration in Finite Terms, Liouville’s Theory of Elementary Methods, Columbia University Press, , New York, N. Y. (1948)
##[8]
J. F. Ritt , Differential algebra, American Mathematical Society Colloquium Publications, Vol. XXXIII, American Mathematical Society, New York, N. Y. (1950)
##[9]
A. B. Shidlovskiĭ, Transcendental numbers, Translated from the Russian by Neal Koblitz, With a foreword by W. Dale Brownawell, De Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin (1989)
##[10]
A. B. Shidlovskiĭ, Transcendence of values of E-functions that are solutions of second-order linear differential equations, (Russian), translated from Mat. Sb, 184 (1993), 75–84 Russian Acad. Sci. Sb. Math., 79 (1994), 63-71
##[11]
P. Sibuya, A remark on Bessel functions, Differential equations, dynamical systems, and control science, Lecture Notes in Pure and Appl. Math., Dekker, New York, 152 (1994), 301-306
##[12]
C. L Siegel, Über einige Anwendungen diophantischer Approximationen, Abhandlungen der Preussischen Akademie der Wissenschaften, Physicalisch mathematische klasse 1929, Nr 1; (German) [On some applications of Diophantine approximations], 81–138, Quad./Monogr., 2, Ed. Norm., Pisa (2014)
##[13]
G. N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, Cambridge, England, The Macmillan Company, New York (1944)
]
Controllability result of nonlinear higher order fractional damped dynamical system
Controllability result of nonlinear higher order fractional damped dynamical system
en
en
In this paper, we investigate the controllability of nonlinear fractional damped dynamical system, which involved fractional
Caputo derivatives of any different orders. In the process of proof, we mainly use the Schaefer’s fixed-point theorem and
Mittag-Leffler matrix function. At last, we give an example to illustrate our main result.
325
337
Junpeng
Liu
School of Mathematics
Jilin University
P. R. China
liujunpeng86619@163.com
Suli
Liu
School of Mathematics
Jilin University
P. R. China
liusl15@mails.jlu.edu.cn
Huilai
Li
School of Mathematics
Jilin University
P. R. China
lihuilai@jlu.edu.cn
Controllability
Mittag-Leffler matrix
Schaefer’s fixed-point theorem
Gramian matrix.
Article.31.pdf
[
[1]
B. N. Achar, J. W. Hanneken, T. Clarke, Response characteristics of a fractional oscillator, Phys. A, 309 (2002), 275-288
##[2]
A. Ahmeda, A. Elgazzar, On fractional order diffusion wave equations model for noniocal epidemics, J. Phys. A Math. Gen., 379 (2007), 607-614
##[3]
O. J. J. Algahtani, Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model, Chaos Solitons Fractals, 89 (2016), 552-559
##[4]
B. S. T. Alkahtani, Chua’s circuit model with Atangana-Baleanu derivative with fractional order, Chaos Solitons Fractals, 89 (2016), 547-551
##[5]
A. Al-rabtah, V. S. Ertürk, S. Momani, Solutions of a fractional oscillator by using differential transform method, Comput. Math. Appl., 59 (2010), 1356-1362
##[6]
A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 20 (2016), 763-769
##[7]
A. Atangana, I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, 89 (2016), 447-454
##[8]
K. Balachandran, V. Govindaraj, M. D. Ortigueira, M. Rivero, J. J. Trujillo, Observability and controllability of fractional linear dynamical systems, In: 6th Workshop on Fractional Dierentiation and Its Applications, France (2013)
##[9]
K. Balachandran, V. Govindaraj, M. Rivero, J. J. Trujillo, Controllability of fractional damped dynamical systems , Appl. Math. Comput., 257 (2015), 66-73
##[10]
K. Balachandran, V. Govindaraj, L. Rodríguez-Germá, J. J. Trujillo, Controllability results for nonlinear fractional-order dynamical systems, J. Optim. Theory Appl., 156 (2013), 33-44
##[11]
K. Balachandran, J. Kokila, On the controllability of fractional dynamical systems, Int. J. Appl. Math. Comput. Sci., 22 (2012), 523-531
##[12]
K. Balachandran, J. Y. Park, J. J. Trujillo, Controllability of nonlinear fractional dynamical systems, Nonlinear Anal., 75 (2012), 1919-1926
##[13]
M. Bettayeb, S. Djennoune, New results on the controllability and observability of fractional dynamical systems, J. Vib. Control, 14 (2008), 1531-1541
##[14]
B. Bonilla, M. Rivero, L. Rodríguez-Germá, J. J. Trujillo, Fractional differential equations as alternative models to nonlinear differential equations, Appl. Math. Comput., 187 (2007), 79-88
##[15]
Y.-Q. Chen, H.-S. Ahn, D.-Y. Xue, Robust controllability of interval fractional order linear time invariant systems, Signal Process., 86 (2006), 2794-2802
##[16]
A. Erdélyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher transcendental functions, McGraw-Hill Book Company, Inc., New York-Toronto-London (1955)
##[17]
S. Guermah, S. Djennoune, M. Bettayeb, Controllability and observability of linear discrete-time fractional-order systems, Int. J. Appl. Math. Comput. Sci., 18 (2008), 213-222
##[18]
R. Hilfer (Ed.), Applications of fractional calculus in physics , World Scientific Publishing Co., Inc., River Edge, NJ (2000)
##[19]
T. Kaczorek, Selected problems of fractional systems theory, Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin (2011)
##[20]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[21]
R. C. Koeller, Applications of fractional calculus to the theory of viscoelasticity, Trans. ASME J. Appl. Mech., 51 (1984), 299-307
##[22]
Y. E. Luchko, M. Rivero, J. J. Trujillo, M. P. Velasco, Fractional models, non-locality, and complex systems, Comput. Math. Appl., 59 (2010), 1048-1056
##[23]
R. Metzler, J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep., 339 (2000), 1-77
##[24]
K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York (1993)
##[25]
C. A. Monje, Y.-Q. Chen, B. M. Vinagre, D.-Y. Xue, V. Feliu, Fractional-order systems and controls. Fundamentals and applications, Advances in Industrial Control. Springer, London (2010)
##[26]
I. Petras, Fractional-order nonlinear systems: modeling, analysis and simulation, Springer Verlag, Berlin Heidelberg (2011)
##[27]
I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
##[28]
D. R. Smart, Fixed point theorems, Cambridge Tracts in Mathematics, Cambridge University Press,, London-New York (1974)
##[29]
A. Tofighi, The intrinsic damping of the fractional oscillator, Phys. A, 329 (2003), 29-34
##[30]
H. Xu, Analytical approximations for a population growth model with fractional order, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 1978-1983
##[31]
K. Yongyong, Z. Xiu’e, Some comparison of two fractional oscillators, Phys. B, 405 (2010), 369-373
##[32]
Y. Zhou, Basic theory of fractional differential equations, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2014)
]