]>
2016
9
1
ISSN 2008-1898
348
Approximating common fixed points for a pair of generalized nonlinear mappings in convex metric space
Approximating common fixed points for a pair of generalized nonlinear mappings in convex metric space
en
en
In this paper, a pair of generalized nonlinear mappings are introduced. Sufficient conditions for the existence
of common fixed points for a pair of generalized nonlinear mappings in convex metric spaces are obtained
and Krasnoselskii type iterations are used to approximate common fixed points. Our results generalize and
extend various known results.
1
7
Chao
Wang
School of Mathematics and Statistics
Nanjing University of Information Science and Technology
P. R. China
wangchaosx@126.com
Taizhong
Zhang
School of Mathematics and Statistics
Nanjing University of Information Science and Technology
P. R. China
ztz@nuist.edu.cn
Nonlinear mappings
common fixed point
convex metric spaces
existence conditions
Krasnoselskii type iterations.
Article.1.pdf
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[1]
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]
Generalized Fractional Integrals Involving Product of Multivariable H-function and a General Class of Polynomials
Generalized Fractional Integrals Involving Product of Multivariable H-function and a General Class of Polynomials
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en
A large number of fractional integral formulas involving certain special functions and polynomials have
been presented. Here, in this paper, we aim at establishing two fractional integral formulas involving the
products of the multivariable H-function and a general class of polynomials by using generalized fractional
integration operators given by Saigo and Maeda [M. Saigo, N. Maeda, Varna, Bulgaria, (1996), 386{400].
All the results derived here being of general character, they are seen to yield a number of results (known
and new) regarding fractional integrals.
8
21
D.
Kumar
Department of Mathematics and Statistics
Jai Narain Vyas University
India
dinesh_dino03@yahoo.com
S. D.
Purohit
Department of Mathematics
Rajasthan Technical University
India
sunil_a_purohit@yahoo.com
J.
Choi
Department of Mathematics
Dongguk University
Republic of Korea
junesang@mail.dongguk.ac.kr
Generalized fractional integral operators
multivariable H-function
general class of polynomials
Mittag-Leffler function.
Article.2.pdf
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[1]
P. Agarwal, Further results on fractional calculus of Saigo operator, Appl. Appl. Math., 7 (2012), 585-594
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P. Agarwal, J. Choi, R. B. Paris , Extended Riemann-Liouville fractional derivative operator and its applications, J. Nonlinear Sci. Appl., 8 (2015), 451-466
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D. Baleanu, P. Agarwal, S. D. Purohit, Certain fractional integral formulas involving the product of generalized Bessel functions, Sci. World J., 2013 (2013), 1-9
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D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus models and numerical methods, 3, Com- plexity, Nonlinearity and Chaos, World Scientific (2012)
##[5]
D. Baleanu, D. Kumar, S. D. Purohit , Generalized fractional integrals of product of two H-functions and a general class of polynomials, Int. J. Comput. Math., 2015 (2015), 1-13
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D. Baleanu, O. G. Mustafa , On the global existence of solutions to a class of fractional differential equations, Comput. Math. Appl., 59 (2010), 1835-1841
##[7]
J. Choi, D. Kumar , Certain unified fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials, J. Inequal. Appl., 2014 (2014), 1-15
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K. C. Gupta, K. Gupta, A. Gupta, Generalized fractional integration of the product of two H-functions, J. Rajasthan Acad. Phys. Sci., 9 (2010), 203-212
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A. A. Kilbas, Fractional calculus of the generalized Wright function, Fract. Calc. Appl. Anal., 8 (2005), 113-126
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A. A. Kilbas, M. Saigo, H-Transforms, theory and applications , Chapman & Hall/CRC Press, Boca Raton (2004)
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A. A. Kilbas, N. Sebastain, Generalized fractional integration of Bessel function of first kind , Integral Transforms Spec. Funct., 19 (2008), 869-883
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D. Kumar, P. Agarwal, S. D. Purohit , Generalized fractional integration of the \(\overline{H}\)-function involving general class of polynomials, Walailak J. Sci. Tech. (WJT), 11 (2014), 1019-1030
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D. Kumar, J. Daiya, Generalized fractional differentiation of the \(\overline{H}\) -function involving general class of polynomials, Int. J. Pure Appl. Sci. Technol., 16 (2013), 42-53
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D. Kumar, S. Kumar, Fractional calculus of the generalized Mittag-Leffler type function, Int. Scholarly Res. Notices, 2014 (2014), 1-5
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A. M. Mathai, R. K. Saxena, H. J. Haubold, The H-function: theory and applications , Springer, New York (2010)
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S. R. Mondal, K. S. Nisar, Marichev-Saigo-Maeda fractional integration operators involving generalized Bessel functions, Math. Probl. Eng., 2014 (2014), 1-11
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T. R. Prabhakar , A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), 7-15
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S. D. Purohit, S. L. Kalla, D. L. Suthar , Fractional integral operators and the multiindex Mittag-Leffler functions , Sci. Ser. A Math. Sci., 21 (2011), 87-96
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S. D. Purohit, D. L. Suthar, S. L. Kalla , Marichev-Saigo-Maeda fractional integration operators of the Bessel function, Matematiche (Catania), 67 (2012), 21-32
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J. Ram, D. Kumar, Generalized fractional integration involving Appell hypergeometric of the product of two H- functions, Vijnana Parishad Anusandhan Patrika, 54 (2011), 33-43
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J. Ram, D. Kumar , Generalized fractional integration of the -function, J. Rajasthan Acad. Phys. Sci., 10 (2011), 373-382
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M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Kyushu Univ., 11 (1978), 135-143
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M. Saigo, N. Maeda, More Generalization of Fractional calculus, Transform Methods and Special Functions, Varna, Bulgaria, (1996), 386-400
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R. K. Saxena, J. Daiya, D. Kumar, Fractional integration of the \(\overline{H}\) -function and a general class of polynomials via pathway operator, J. Indian Acad. Math., 35 (2013), 261-274
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R. K. Saxena, J. Ram, D. Kumar, Generalized fractional integration of the product of Bessel functions of the first kind, Proceedings of the 9th Annual Conference, Soc. Spec. Funct. Appl., 9 (2011), 15-27
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R. K. Saxena, J. Ram, D. L. Suthar, Fractional calculus of generalized Mittag-Leffler functions, J. Indian Acad. Math., 31 (2009), 165-172
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R. K. Saxena, M. Saigo, Generalized fractional calculus of the H-function associated with the Appell function F3, J. Fract. Calc., 19 (2001), 89-104
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H. M. Srivastava, K. C. Gupta, S. P. Goyal , The H-functions of one and two variables with applications, South Asian Publishers, New Delhi/Madras (1982)
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H. M. Srivastava, R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables I, Comment. Math. Univ. St. Paul., 24 (1975), 119-137
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H. M. Srivastava, R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables II, Comment Math. Univ. St. Paul., 25 (1976), 167-197
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H. M. Srivastava, R. K. Saxena, Operators of fractional integration and their applications, Appl. Math. Comput., 118 (2001), 1-52
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H. M. Srivastava, R. K. Saxena, J. Ram , Some multidimensional fractional integral operators involving a general class of polynomials, J. Math. Anal. Appl., 193 (1995), 373-389
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H. M. Srivastava, N. P. Singh , The integration of certain product of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo, 32 (1983), 157-187
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J. Zhao, Positive solutions for a class of q-fractional boundary value problems with p-Laplacian, J. Nonlinear Sci. Appl., 8 (2015), 442-450
]
Fixed point theorems for \((\alpha,\beta)-(\psi,\varphi)\)-contractive mapping in b--metric spaces with some numerical results and applications
Fixed point theorems for \((\alpha,\beta)-(\psi,\varphi)\)-contractive mapping in b--metric spaces with some numerical results and applications
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en
In this paper, we introduce the concept of \((\alpha,\beta)-(\psi,\varphi)\)-contractive mapping in b-metric spaces. We establish
some fixed point theorems for such mappings and also give an example supporting our results. Finally, we
apply our main results to prove a fixed point theorem involving a cyclic mapping.
22
33
Oratai
Yamaod
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
oratai_eve@hotmail.com
Wutiphol
Sintunavarat
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
wutiphol@mathstat.sci.tu.ac.th; poom_teun@hotmail.com
\(b\)-metric space
cyclic \((\alpha،\beta)\)-admissible mapping
\((\alpha،\beta)-(\psi،\varphi)\)-contractive mapping.
Article.3.pdf
[
[1]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960
##[2]
S. Alizadeh, F. Moradlou, P. Salimi, Some fixed point results for \((\alpha,\beta)-(\psi,\phi)\)-contractive mappings, Filomat, 28 (2014), 635-647
##[3]
M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math, 8 (2010), 367-377
##[4]
M. Bota, A. Molnar, V. Csaba, On Ekeland's variational principle in b-metric spaces, Fixed Point Theory, 12 (2011), 21-28
##[5]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[6]
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276
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M. S. Khan, M. Swaleh, S. Sessa , Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9
##[8]
W. A. Kirk, P. S. Srinivasan, P. Veeramani , Fixed points for mappings satisfying cyclical contractive conditions , Fixed Point Theory, 4 (2003), 79-89
]
Common fixed point theorems for weakly C-contractive mappings in ordered partial metric spaces
Common fixed point theorems for weakly C-contractive mappings in ordered partial metric spaces
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en
In this paper, we investigate some common fixed point theorems for weakly C-contractive mappings in
ordered partial metric spaces. Presented theorems generalize the results of Karapınar and Shatanawi [E.
Karapınar, W. Shatanawi, Abstr. Appl. Anal., 2012 (2012), 17 pages]. An example is also given to support
our main result.
34
45
Chunfang
Chen
Department of Mathematics
Nanchang University
P. R. China
ccfygd@sina.com
Yaqiong
Gu
Department of Mathematics
Nanchang University
P. R. China
924756324@qq.com
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
Fixed point
common fixed point
partial metric space
weakly C-contraction.
Article.4.pdf
[
[1]
M. Abbas, T. Nazir, Fixed point of generalize weakly contractive mappings in ordered partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-19
##[2]
T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54 (2011), 2923-2927
##[3]
T. Abedeljawad, E. Karapınar, K. Tas, Common fixed point theorems in cone Banach spaces , Hacet. J. Math. Stat., 40 (2011), 211-217
##[4]
T. Abdeljawad, E. Karapınar, K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
##[5]
T. Abdeljawad, E. Karapınar, K. Tas, A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716-719
##[6]
M. Akram, W. Shamaila, A coincident point and common fixed point theorem for weakly compatible mappings in partial metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 184-192
##[7]
I. Altun, H. Sims , Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., 2010 (2010), 1-17
##[8]
S. M. Alsulami, Unique Coincidence and Fixed Point Theorem for g-Weakly C-Contractive Mappings in Partial Metric Spaces, Abstr. Appl. Anal., 2014 (2014), 1-6
##[9]
C. F. Chen, C. X. Zhu , Fixed point theorems for weakly C-contractive mappings in partial metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-16
##[10]
J. H. Chen, X. J. Huang, Fixed point theorems for fuzzy mappings in metric spaces with an application, J. Inequal. Appl., 2015 (2015), 1-21
##[11]
J. H. Chen, X. J. Huang, Coupled fixed point theorems for compatible mappings in partially ordered G-metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 130-141
##[12]
J. H. Chen, X. J. Huang, Quadruple fixed point theorems under (\(\varphi,\psi\))- contractive conditions in partially ordered G-metric spaces with mixed g-monotone property, J. Nonlinear Sci. Appl., 8 (2015), 285-300
##[13]
B. S. Choudhury, Unique fixed point theorem for weak C-contractive mappings, Kathmandu Univ. J. Sci. Eng. Tech., 5 (2009), 6-13
##[14]
R. H. Haghi, S. Rezapour, N. Shahzad , Be careful on partial metric fixed point results , Topology Appl., 160 (2013), 450-454
##[15]
J. Harjani, B.López, K.sadarangani, Fixed point theorems for weakly C-contractive mappings in ordered metric spaces, Comput. Math. Appl., 61 (2011), 790-796
##[16]
X. J. Huang, C. X. Zhu, X. Wen, Fixed point theorems for expanding mappings in partial metric spaces, An. Stiint. Univ. , 20 (2013), 213-224
##[17]
D. Ilic, V. pavlovic, V. Rakocevic, Some new extensions of Bananch's contraction principle to partial metric space, Appl. Math. Lett., 24 (2011), 1326-1330
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M. Imdad, A. Sharma, A. Erduran, Generalized Meir-Keeler type n-tupled fixed point theorems in ordered partial metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-24
##[19]
E. Karapınar, Inci M. Erhan , Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894-1899
##[20]
E. Karapınar, W. Shatanawi, On weakly (\(C,\psi,\phi\))-contractive mappings in ordered partial metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-17
##[21]
M. S. Khan, M. Swaleh, S. Sessa , Fixed point theorems by altering distances between the points , Bull. Aust. Math. Soc., 30 (1984), 1-9
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S. G. Matthews, Partial metric topology , Research Report 212, Dept. of Computer Science, University of Warwick (1992)
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S. G. Matthews , Partial metric topology, in: Pro. 8th Summer Conference on General Toplogy and Applications, Ann. New York Acad. Sci., 728 (1994), 183-197
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H. K. Nashine, Z. Kadelburg, S. Radenović , Common fixed point theorems for weakly isotone increasing mappings on ordered partial metric spaces, Math. Comput. Model., 57 (2013), 2355-2365
##[25]
H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Model., 54 (2011), 712-720
##[26]
T. Nazir, M. Abbas , Common fixed points of two pairs of mappings satisfying (E.A)-property in partial metric spaces, J. Inequal. Appl., 2014 (2014), 1-12
##[27]
W. Shatanawi , Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces, Math. Comput. Model., 54 (2011), 2816-2826
##[28]
N. Shahzad, O. Valero, A Nemytskii-Edelstein type fixed point theorem for partial metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-15
]
Impulsive first-order functional \(q_k\)-integro-difference inclusions with boundary conditions
Impulsive first-order functional \(q_k\)-integro-difference inclusions with boundary conditions
en
en
In this paper, we discuss the existence of solutions for a first order boundary value problem for impulsive
functional \(q_k\)-integro-difference inclusions. Some new existence results are obtained for convex as well as
non-convex multivalued maps with the aid of some classical fixed point theorems. Illustrative examples are
also presented.
46
60
Jessada
Tariboon
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Thailand
jessada.t@sci.kmutnb.ac.th
Sotiris K.
Ntouyas
Department of Mathematics
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
University of Ioannina
King Abdulaziz University
Greece
Saudi Arabia
sntouyas@uoi.gr
Weerawat
Sudsutad
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Thailand
wrw.sst@gmail.com
\(q_k\)-derivative
\(q_k\)-integral
impulsive \(q_k\)-difference inclusions
existence
fixed point theorem.
Article.5.pdf
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[1]
R. P. Agarwal, Y. Zhou, Y. He , Existence of fractional neutral functional differential equations, Comput. Math. Appl., 59 (2010), 1095-1100
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B. Ahmad, Boundary-value problems for nonlinear third-order q-difference equations, Electron. J. Differential Equ., 2011 (2011), 1-7
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B. Ahmad, A. Alsaedi, S. K. Ntouyas , A study of second-order q-difference equations with boundary conditions, Adv. Difference Equ., 2012 (2012), 1-10
##[4]
B. Ahmad, J. J. Nieto , Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Bound. Value Probl., 2011 (2011), 1-9
##[5]
B. Ahmad, J. J. Nieto, On nonlocal boundary value problems of nonlinear q-difference equations , Adv. Difference Equ., 2012 (2012), 1-10
##[6]
B. Ahmad, J. J. Nieto, Boundary value problems for a class of sequential integrodifferential equations of fractional order, J. Funct. Spaces Appl., 2013 (2013), 1-8
##[7]
B. Ahmad, S. K. Ntouyas, Boundary value problems for q-difference inclusions, Abstr. Appl. Anal., 2011 (2011), 1-15
##[8]
B. Ahmad, S. K. Ntouyas, A. Alsaedi , New existence results for nonlinear fractional differential equations with three-point integral boundary conditions, Adv. Difference Equ., 2011 (2011), 1-11
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B. Ahmad, S. K. Ntouyas, A. Alsaedi, A study of nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type multistrip boundary conditions, Math. Probl. Eng., 2013 (2013), 1-9
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B. Ahmad, S. K. Ntouyas, I. K. Purnaras, Existence results for nonlinear q-difference equations with nonlocal boundary conditions, Comm. Appl. Nonlinear Anal., 19 (2012), 59-72
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D. Băleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus models and numerical methods, Series on complexity, nonlinearity and chaos, World Scientific, Boston (2012)
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D. Băleanu, O. G. Mustafa, R. P. Agarwal, On \(L^p\)-solutions for a class of sequential fractional differential equations, Appl. Math. Comput., 218 (2011), 2074-2081
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M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, New York (2006)
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M. El-Shahed, H. A. Hassan , Positive solutions of q-difference equation, Proc. Amer. Math. Soc., 138 (2010), 1733-1738
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M. Frigon , Théorémes d'existence de solutions d'inclusions différentielles, Topological methods in differential equations and inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Kluwer Acad. Publ. Dordrecht, 472 (1995), 51-87
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S. Hu, N. Papageorgiou , Handbook of multivalued analysis, Theory I, Kluwer, Dordrecht (1997)
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V. Kac, P. Cheung, , Quantum calculus, Springer, New York (2002)
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo , Theory and applications of fractional differential equations, NorthHolland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam (2006)
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X. Liu, M. Jia, W. Ge, Multiple solutions of a p-Laplacian model involving a fractional derivative, Adv. Difference Equ., 2013 (2013), 1-12
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D. O'Regan, S. Staněk , Fractional boundary value problems with singularities in space variables, Nonlinear Dynam., 71 (2013), 641-652
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I. Podlubny, Fractional differential equations, Academic Press, San Diego (1998)
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S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, theory and applications, Gordon and Breach, Yverdon (1993)
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A. M. Samoilenko, N. A. Perestyuk, Impulsive differential equations, World Scientific, Singapore (1995)
##[32]
J. Tariboon, S. K. Ntouyas, Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ., 2013 (2013), 1-19
##[33]
J. Tariboon, S. K. Ntouyas, Boundary value problem for first-order impulsive functional q-integrodifference equations, Abstr. Appl. Anal., 2014 (2014), 1-11
##[34]
W. Zhou, H. Liu, Existence solutions for boundary value problem of nonlinear fractional q-difference equations, Adv. Difference Equ., 2013 (2013), 1-12
]
Algorithms for the variational inequalities and fixed point problems
Algorithms for the variational inequalities and fixed point problems
en
en
A system of variational inequality and fixed point problems is considered. Two algorithms have been
constructed. Our algorithms can find the minimum norm solution of this system of variational inequality
and fixed point problems.
61
74
Yaqiang
Liu
School of Management
Tianjin Polytechnic University
China
yani3115791@126.com
Zhangsong
Yao
School of Information Engineering
Nanjing Xiaozhuang University
China
yaozhsong@163.com
Yeong-Cheng
Liou
Department of Information Management
Center for General Education
Cheng Shiu University
Kaohsiung Medical University
Taiwan
Taiwan
simplex_liou@hotmail.com
Li-Jun
Zhu
School of Mathematics and Information Science
Beifang University of Nationalities
China
zhulijun1995@sohu.com
Variational inequality
monotone mapping
nonexpansive mapping
fixed point
minimum norm.
Article.6.pdf
[
[1]
J. Y. Bello Cruz, A. N. Iusem, Convergence of direct methods for paramonotone variational inequalities, Comput. Optim. Appl., 46 (2010), 247-263
##[2]
A. Cabot , Proximal point algorithm controlled by a slowly vanishing term: applications to hierarchical minimization, SIAM J. Optim., 15 (2005), 555-572
##[3]
L. C. Ceng, C. Wang, J. C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Methods Oper. Res., 67 (2008), 375-390
##[4]
Y. Censor, A. Gibali, S. Reich , The subgradient extragradient method for solving variational inequalities in Hilbert space, J. Optim. Theory Appl., 148 (2011), 318-335
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A Laplace type problem for three lattices with non-convex cell
A Laplace type problem for three lattices with non-convex cell
en
en
In this paper we consider three lattices with cells represented in Fig. 1, 3 and 5 and we determine the
probability that a random segment of constant length intersects a side of lattice.
75
82
Giuseppe
Caristi
Department S. E. A. M.
University of Messina
Italy
gcaristi@unime.it
Maria
Pettineo
Department of Mathematics and Informatics
University of Palermo
Italy
maria.pettineo@unipa.it
Marius
Stoka
Sciences Accademy of Turin
Italy
marius.stoka@gmail.com
Geometric probability
stochastic geometry
random sets
random convex sets and integral geometry.
Article.7.pdf
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[1]
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Fixed point theorems for partial \(\alpha-\psi\) contractive mappings in generalized metric spaces
Fixed point theorems for partial \(\alpha-\psi\) contractive mappings in generalized metric spaces
en
en
In this paper, we introduce the concept of partial \(\alpha-\psi\) contractive mappings along with generalized metric
distance. We also establish the existence of fixed point theorems for such mappings in generalized metric
spaces. Our results extend and unify main results of Karapinar [E. Karapinar, Abstr. Appl. Anal., 2014
(2014), 7 pages] and several well-known results in literature. We give some examples to illustrate the
usability of our results. Moreover, we prove the fixed point results in generalized metric space endowed with
an arbitrary binary relation and the fixed point results in generalized metric space endowed with graph.
83
91
Aphinat
Ninsri
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
aphinatninsri@gmail.com
Wutiphol
Sintunavarat
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
wutiphol@mathstat.sci.tu.ac.th; poom_teun@hotmail.com
Fixed point theory
partial \(\alpha-\psi\) contractive mappings
generalized metric spaces
binary relation.
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[1]
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37
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The upper bound estimation for the spectral norm of \(r\)-circulant and symmetric \(r\)-circulant matrices with the Padovan sequence
The upper bound estimation for the spectral norm of \(r\)-circulant and symmetric \(r\)-circulant matrices with the Padovan sequence
en
en
In this paper, we gives an upper bound estimation of the spectral norm for matrices \(A\) and \(B\) such that the
entries in the first row of \(n\times n\) \(r\)-circulant matrix \(A = Circ_r(a_1; a_2; ...; a_n)\) and \(n\times n\) symmetric \(r\)-circulant
matrix \(B = SCirc_r(a_1; a_2; ...; a_n)\) are \(a_i = P_i\) or \(a_i = P^2
_i\) or \(a_i = P_{i-1}\) or \(a_i = P^2_{i-1}\), where \(\{P_i\}^\infty_{i
=0}\) is
Padovan sequence. At the last section, some illustrative numerical example is furnished which demonstrate
the validity of the hypotheses and degree of utility of our results.
92
101
Wutiphol
Sintunavarat
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
wutiphol@mathstat.sci.tu.ac.th; poom_teun@hotmail.com
r-circulant matrices
symmetric r-circulant matrices
Padovan sequence
Hadamard product.
Article.9.pdf
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[1]
C. He, J. Ma, K. Zhang, Z. Wang , The upper bound estimation on the spectral norm of r-circulant matrices with the Fibonacci and Lucas numbers, J. Inequal. Appl., 2015 (2015), 1-10
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]
Center and pseudo-isochronous conditions in a quasi analytic system
Center and pseudo-isochronous conditions in a quasi analytic system
en
en
The center conditions and pseudo-isochronous center conditions at origin or infinity in a class of non-analytic
polynomial differential system are classified in this paper. By proper transforms, the quasi analytic system
can be changed into an analytic system, and then the first 77 singular values and periodic constants are
computed by Mathematics. Finally, we investigate the center conditions and pseudo-isochronous center
conditions at infinity for the system. Especially, this system was investigated when \(\lambda = 1\) in [Y. Wu, W.
Huang, H. Dai, Qual. Theory Dyn. Syst., 10 (2011), 123{138].
102
111
Zheng
Qingyu
School of Science
Linyi University
China
zhengqingyu@lyu.edu.cn
Li
Hongwei
School of Science
Linyi University
China
hongweifx@163.com
Infinity
quasi analytic
center
pseudo-isochronicity.
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]
On the extensions of the almost convergence idea and core theorems
On the extensions of the almost convergence idea and core theorems
en
en
The sequence spaces \(rf\) and \(rf_0\), more general and comprehensive than the almost convergent sequence spaces
\(f\) and \(f_0\), were introduced by Zararsız and Şengönül in [Z. Zararsız, M. Şengönül, Doctoral Thesis, Nevşehir,
(2015)]. The purpose of the present paper is to study the sequence spaces \(brf\) and \(brf_0\), that is, the sets of all
sequences such that their \(B(r; s)\) transforms are in \(rf\) and \(rf_0\) respectively. Furthermore, we determine the
\(\beta\)- and
\(\gamma\)- duals of brf, we show that there exists a linear isomorphic mapping between the spaces \(rf\) and \(brf\),
and between \(rf_0\) and \(brf_0\) respectively, and provide some matrix characterizations of these spaces. Finally,
we introduce the \(B_{RB}\)-core of a complex valued sequence and prove some theorems related to this new
type of core.
112
125
Zarife
Zararsiz
Department of Mathematics
Nevşehir Hacı Bektaş Veli University
Turkey
zarifezararsiz@nevsehir.edu.tr
Almost convergence
\(\beta\)- and \(\gamma\)-duals
matrix domain of a sequence space
isomorphism
core theorem.
Article.11.pdf
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[1]
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B. Altay, F. Başar , Generalization of the sequence space \(\ell(p)\) derived by weighted mean, J. Math. Anal. Appl., 330 (2007), 174-185
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B. Altay, F. Başar, The fine spectrum and the matrix domain of the difference operator \(\Delta\) on the sequence space \(\ell_p, (0 < p < 1)\), Commun. Math. Anal., 2 (2007), 1-11
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]
A topological analysis of high-contrast patches in natural images
A topological analysis of high-contrast patches in natural images
en
en
In this paper, we study qualitative topological analysis of spaces of natural images locally. We apply the
techniques of computational topology to the space of 3×3, 4×4, 5×5, 6×6 and 7×7 high-contrast patches.
We show that in each case there is a subspace of the space of all high-contrast patches that is topologically
equivalent to the Klein bottle and we found that the size of the largest subspace having the Klein bottle’s
homology decreases with increasing of the size of patches. The data sets used in this paper are different
from that discussed in the paper ”on the local behavior of spaces of natural images”, we conformed our
findings by applying the same methods to the different sizes patches.
126
138
Shengxiang
Xia
College of Science
Shandong Jianzhu University
P. R. China
xias@sdjzu.edu.cn
Topology
persistent homology
natural images
high-contrast patches
Klein bottle
barcode.
Article.12.pdf
[
[1]
H. Adams, G. Carlsson , On the nonlinear statistics of range image patches, SIAM J. Imaging Sci., 2 (2009), 110-117
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H. Adams, A. Tausz, Javaplex tutorial, Available on the internet (http://goo.gl/5uaRoQ), (2015)
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G. Carlsson, Topology and data, Bull. Amer. Math. Soc., 46 (2009), 255-308
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G. Carlsson, T. Ishkhanov, V. de Silva, A. Zomorodian, On the local behavior of spaces of natural images, Int. J. Comput. Vis., 76 (2008), 1-12
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V. de Silva, G. Carlsson, Topological estimation using witness complexes, Proc. Sympos. Point-Based Graphics, (2004), 157-166
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H. Edelsbrunner, D. Letscher, A. Zomorodian, Topological persistence and simplification, Discrete Comput. Geom., 28 (2002), 511-533
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H. Jegou, M. Douze, C. Schmid , Hamming embedding and weak geometry consistency for large scale image search , Proc. of the 10th Europ. conf. on Computer vision, (2008), 304-317
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A. B. Lee, K. S. Pedersen, D. Mumford , The non-linear statistics of high-contrast patches in natural images, Int. J. Comput. Vis., 54 (2003), 83-103
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]
Some inequalities of Hermite--Hadamard type for functions whose second derivatives are boldsymbol (\(\alpha,m\))-convex
Some inequalities of Hermite--Hadamard type for functions whose second derivatives are boldsymbol (\(\alpha,m\))-convex
en
en
In the paper, the authors establish a new integral identity and by this identity with the Hölder integral
inequality, discover some new Hermite-Hadamard type integral inequalities for functions whose second
derivatives are (\(\alpha,m\))-convex.
139
148
Ye
Shuang
College of Mathematics
Inner Mongolia University for Nationalities
China
shuangye152300@sina.com
Feng
Qi
Department of Mathematics, College of Science
Tianjin Polytechnic University
China
qifeng618@gmail.com; qifeng618@hotmail.com
Yan
Wang
College of Mathematics
Inner Mongolia University for Nationalities
China
sella110@vip.qq.com
second derivative
Hermite-Hadamard type inequality
(\(\alpha،m\))-convex function
Hölder integral inequality.
Article.13.pdf
[
[1]
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]
Fixed Point Methods for Solving Solutions of a Generalized Equilibrium Problem
Fixed Point Methods for Solving Solutions of a Generalized Equilibrium Problem
en
en
In this paper, a generalized equilibrium problem is investigated based on fixed point methods. Strong
convergence theorems of solutions are established in the framework of Hilbert spaces.
149
159
Lingmin
Zhang
Institute of Mathematics and Information Technology
Hebei Normal University of Science and Technology
China
zhanglm103@126.com
Yan
Hao
School of Mathematics, Physics and Information Science
Zhejiang Ocean University
China
zjhaoyan@aliyun.com
Equilibrium problem
nonexpansive mapping
fixed point
variational inequality.
Article.14.pdf
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Solvability for integral boundary value problems of fractional differential equation on infinite intervals
Solvability for integral boundary value problems of fractional differential equation on infinite intervals
en
en
In this paper, we establish the solvability for integral boundary value problems of fractional differential
equation with the nonlinear term dependent in a fractional derivative of lower order on infinite intervals.
The existence and uniqueness of solutions for the boundary value problem are proved by means of the
Schauder's fixed point theorem and Banach's contraction mapping principle. Finally, we give two examples
to demonstrate the use of the main results.
160
170
Changlong
Yu
College of Sciences
Hebei University of Science and Technology
P. R. China
changlongyu@126.com
Jufang
Wang
College of Sciences
Hebei University of Science and Technology
P. R. China
wangjufang1981@126.com
Yanping
Guo
College of Sciences
Hebei University of Science and Technology
P. R. China
guoyanping65@126.com
Integral boundary value problem
fractional difierential equation
infinite interval
Fixed point theorem.
Article.15.pdf
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]
Robust stability analysis of uncertain T-S fuzzy systems with time-varying delay by improved delay-partitioning approach
Robust stability analysis of uncertain T-S fuzzy systems with time-varying delay by improved delay-partitioning approach
en
en
This paper focuses on the robust stability criteria of uncertain T-S fuzzy systems with time-varying delay
by an improved delay-partitioning approach. An appropriate augmented Lyapunov-Krasovskii functional
(LKF) is established by partitioning the delay in all integral terms. Since the relationship between each
subinterval and time-varying delay has been taken a full consideration, and some tighter bounding inequalities
are employed to deal with (time-varying) delay-dependent integral items of the derivative of LKF,
less conservative delay-dependent stability criteria can be expected in terms of \(e_s\) and LMIs. Finally, two
numerical examples are provided to show that the proposed conditions are less conservative than existing
ones.
171
185
Jun
Yang
College of Computer Science
Civil Aviation Flight University of China
P. R. China
yj_uestc@126.com
Wen-Pin
Luo
College of Science
Sichuan University of Science and Engineering
P. R. China
Kai-Bo
Shi
Department of Applied Mathematics
University of Waterloo
Canada N2L 3G1
Xin
Zhao
Postgraduate Department
Civil Aviation Flight University of China
P. R. China
T-S fuzzy systems
time-varying delay
delay-partitioning approach
stability
Lyapunov-Krasovskii functional (LKF)
linear matrix inequalities (LMIs).
Article.16.pdf
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J. An, G. Wen, Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach, Fuzzy Sets and Systems, 185 (2011), 83-94
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O. M. Kwon, M. J. Park, S. M. Lee, J. H. Park , Augmented Lyapunov-Krasovskii functional approaches to robust stability criteria for uncertain Takagi-Sugeno fuzzy systems with time-varying delays, Fuzzy Sets and Systems, 201 (2012), 1-19
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C. Peng, M. R. Fei , An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay, Fuzzy Sets and Systems, 212 (2013), 97-109
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C. Peng, L. Y. Wen, J. Q. Yang , On delay-dependent robust stability criteria for uncertain T-S fuzzy systems with interval time-varying delay, Int. J. Fuzzy Syst., 13 (2011), 35-44
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]
Existence and uniqueness of the weak solution for a contact problem
Existence and uniqueness of the weak solution for a contact problem
en
en
We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless
contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory,
the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we
derive the classical variational formulation of the model which is given by a system coupling an evolutionary
variational equality for the displacement field, a time-dependent variational equation for the potential field
and a differential equation for the bounding field. Then we prove the existence of a unique weak solution
for the model. The proof is based on arguments of evolution equations and the Banach fixed point theorem.
186
199
Amar
Megrous
Department of Mathematics
EPSE-CSG
Algeria
megrous.amar@yahoo.com
Ammar
Derbazi
Faculty of MI, Department of Mathematics
University Bordj BBA
Algeria
aderbazi@yahoo.fr
Mohamed
Dalah
Faculty of Exactes Sciences: FSE, Department of Mathematics
University Mentouri of Constantine
Algeria
dalah.mohamed@yahoo.fr
Weak solution
variational formulation
Banach fixed point theorem
variational inequality
evolution equations.
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]
Stability of a nonlinear Volterra integro-differential equation via a fixed point approach
Stability of a nonlinear Volterra integro-differential equation via a fixed point approach
en
en
The object of the present paper is to examine the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability
of a nonlinear Volterra integro-differential equation by using the fixed point method.
200
207
Sebaheddin
Şevgin
Faculty of Sciences, Department of Mathematics
Yuzuncu Yil University
Turkey
ssevgin@yahoo.com
Hamdullah
Şevli
Department of Mathematics, Faculty of Sciences and Arts
Istanbul Commerce University
Turkey
hsevli@yahoo.com
Hyers-Ulam stability
Hyers-Ulam-Rassias stability
Volterra integro-differential equations
fixed-point method.
Article.18.pdf
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[1]
M. Akkouchi, Hyers-Ulam-Rassias stability of nonlinear Volterra integral equations via a fixed point approach , Acta Univ. Apulensis Math. Inform., 26 (2011), 257-266
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J. R. Morales, E. M. Rojas, Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay, Int. J. Nonlinear Anal. Appl., 2 (2011), 1-6
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S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, Inc., New York (1964)
]
Blow-up for a degenerate and singular parabolic equation with nonlocal boundary condition
Blow-up for a degenerate and singular parabolic equation with nonlocal boundary condition
en
en
The purpose of this work is to deal with the blow-up behavior of the nonnegative solution to a degenerate
and singular parabolic equation with nonlocal boundary condition. The conditions on the existence and
non-existence of the global solution are given. Further, under some suitable hypotheses, we discuss the
blow-up set and the uniform blow-up profile of the blow-up solution.
208
218
Dengming
Liu
School of Mathematics and Computational Science
Hunan University of Science and Technology
People's Republic of China
liudengming08@163.com
Degenerate and singular parabolic equation
global existence
blow-up
blow-up set
uniform blow-up profile.
Article.19.pdf
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]
Positive solutions for Sturm-Liouville eigenvalue problems
Positive solutions for Sturm-Liouville eigenvalue problems
en
en
By means of the lower and upper solutions argument and fixed index theorem in the frame of the ODE technique, we consider the existence and nonexistence of multiple positive solutions for fourth-order eigenvalue
Sturm-Liouville boundary value problem. Our results significantly extend and improve many known results
including singular and nonsingular cases.
.
219
230
Hua
Su
School of Mathematics and Quantitative Economics
Shandong University of Finance and Economics
China
jnsuhua@163.com
Qiuju
Tuo
School of Mathematics and Quantitative Economics
Shandong University of Finance and Economics
China
sdusuh@163.com
Fourth-order singular differential equation
lower and upper solutions
positive solutions
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]
A new approach in handling soft decision making problems
A new approach in handling soft decision making problems
en
en
The goal of this paper is to bring a new approach to the computation of the decision making problems by
using inverse (fuzzy) soft sets instead of (fuzzy) soft sets which makes the algorithms easier and faster than
the existed methods. For this purpose, we first define inverse soft sets and inverse fuzzy soft sets. Then we
use them to solve decision making problems in a slightly modified way.
231
239
Vildan
Çetkin
Department of Mathematics
Kocaeli University, Umuttepe Campus
Turkey
vcetkin@gmail.com
Abdülkadir
Aygünoǧlu
Department of Mathematics
Kocaeli University, Umuttepe Campus
Turkey
aygunoglu@gmail.com
Halis
Aygün
Department of Mathematics
Kocaeli University, Umuttepe Campus
Turkey
halis@kocaeli.edu.tr
Inverse soft set
inverse fuzzy soft set
comparison table
decision making.
Article.21.pdf
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]
A unique fixed point result using generalized contractive conditions on cyclic mappings in partial metric spaces
A unique fixed point result using generalized contractive conditions on cyclic mappings in partial metric spaces
en
en
The purpose of this paper is to study fixed point result for generalized contractive condition on cyclic
mappings in complete partial metric spaces. The effectiveness of the result is also illustrated through an
example.
240
246
W.
Shamaila
Department of Mathematics
Kinnaird College for Women
Pakistan
shamailawaheed20@gmail.com
M.
Akram
College of Science, Department of Mathematics and Statistics
Department of Mathematics
King Faisal University
GC University
Saudi Arabia
Pakistan
maahmed@kfu.edu.sa; dr.makram@gcu.edu.pk
Cyclic Mappings
generalized contractions
partial metric spaces
common fixed point.
Article.22.pdf
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[1]
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H. Aydi, E. Karapinar, A Meir-Keeler common type fixed point theorem on partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-10
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M. A. Petric, Some results concerning cyclical contractive mappings, General Math., 18 (2010), 213-226
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]
Additive \(\rho\)-functional inequalities in normed spaces
Additive \(\rho\)-functional inequalities in normed spaces
en
en
In this paper, we solve the additive \(\rho\)-functional inequalities
\[ \| f(x + y) - f(x) - f(y)\| \leq\left\|\rho\left(2f(\frac{x+y}{2})-f(x)-f(y)\right)\right\|\quad\quad (1)\]
and
\[\left\|\left(2f(\frac{x+y}{2})-f(x)-f(y)\right)\right\|\leq \| \rho (f(x + y) - f(x) - f(y))\| \quad\quad (2)\]
where \(\rho\) is a number with \(|\rho|< 1\) . Using the fixed point method, we prove the Hyers-Ulam stability of the
additive functional inequalities (1) and (2) in normed spaces.
247
253
Jiyun
Choi
Mathematics Branch
Seoul Science High School
Korea
jiyoonthink@naver.com
Juno
Seong
Mathematics Branch
Seoul Science High School
Korea
juno10290@naver.com
Choonkill
Park
Research Institute for Natural Sciences
Hanyang University
Korea
baak@hanyang.ac.kr
Additive \(\rho\)-functional inequality
fixed point
Hyers-Ulam stability.
Article.23.pdf
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D. Shin, C. Park, S. Farhadabadi, On the superstability of ternary Jordan \(C^*\)-homomorphisms, J. Comput. Anal. Appl., 16 (2014), 964-973
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D. Shin, C. 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
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S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York (1960)
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C. Zaharia, On the probabilistic stability of the monomial functional equation, J. Nonlinear Sci. Appl., 6 (2013), 51-59
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]
Hybrid algorithms for a family of pseudocontractive mappings
Hybrid algorithms for a family of pseudocontractive mappings
en
en
In this paper, we present an iterative algorithm with hybrid technique for a family of pseudocontractive
mappings. It is shown that the suggested algorithm strongly converges to a common fixed point of a family
of pseudocontractive mappings.
254
261
Chongyang
Luo
Department of Mathematics
Tianjin Polytechnic University
China
luochongyang@aliyun.com
Yonghong
Yao
Department of Mathematics
Tianjin Polytechnic University
China
yaoyonghong@aliyun.com
Zhangsong
Yao
School of Information Engineering
Nanjing Xiaozhuang University
China
yaozhsong@163.com
Yeong-Cheng
Liou
Department of Information Management
Center for General Education
Cheng Shiu University
Kaohsiung Medical University
Taiwan
Taiwan
simplex_liou@hotmail.com
Pseudocontractive mappings
hybrid algorithms
fixed point
strong convergence
Article.24.pdf
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[1]
A. E. Al-Mazrooei, A. S. M. Alofi, A. Latif, J. C. Yao, Generalized mixed equilibria, variational inclusions and fixed point problems, Abstr. Appl. Anal., 2014 (2014), 1-16
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V. Berinde, Iterative approximation of fixed points, Lecture Notes in Mathematics, Springer, Berlin (2007)
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L. C. Ceng, C. W. Liao, C. T. Pang, C. F. Wen, Convex minimization with constraints of systems of variational inequalities, mixed equilibrium, variational inequality, and fixed point problems, J. Appl. Math., 2014 (2014), 1-28
##[4]
L. C. Ceng, C. W. Liao, C. T. Pang, C. F. Wen, Multistep hybrid iterations for systems of generalized equilibria with constraints of Several problems, Abst. Appl. Anal., 2014 (2014), 1-27
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L. C. Ceng, A. Petrusel, J. C. Yao , Strong Convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudocontractive mappings, Appl. Math. Comput., 209 (2009), 162-176
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C. E. Chidume, H. Zegeye, Approximate fixed point sequences and convergence theorems for Lipschitz pseudo- contractive maps, Proc. Amer. Math. Soc., 132 (2004), 831-840
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S. Y. Cho, X. Qin, S. M. Kang , Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions, Appl. Math. Lett., 25 (2012), 854-857
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C. Matinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal., 64 (2006), 2400-2411
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N. Nadezhkina, W. Takahashi, Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings, SIAM J. Optim., 16 (2006), 1230-1241
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E. U. Ofoedu, H. Zegeye, Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces, J. Math. Anal. Appl., 372 (2010), 68-76
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A. Udomene , Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudo- contractions in Banach spaces, Nonlinear Anal., 67 (2007), 2403-2414
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Y. Yao, Y. C. Liou, R. Chen , Strong convergence of an iterative algorithm for pseudo-contractive mapping in Banach spaces, Nonlinear Anal., 67 (2007), 3311-3317
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Y. Yao, Y. C. Liou, G. Marino, A hybrid algorithm for pseudo-contractive mappings, Nonlinear Anal., 71 (2009), 4997-5002
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H. Zegeye, N. Shahzad, M. A. Alghamdi , Minimum-norm fixed point of pseudocontractive mappings, Abst. Appl. Anal., 2012 (2012), 1-15
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Q. B. Zhang, C. Z. Cheng, Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space, Math. Comput. Modelling, 48 (2008), 480-485
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H. Zhou, Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces, Nonlinear Anal., 70 (2009), 4039-4046
]
Cone-adapted continuous shearlet transform and reconstruction formula
Cone-adapted continuous shearlet transform and reconstruction formula
en
en
The shearlet system generated by unitary representation of the shearlet group becomes unattractive due to
biasedness towards one axis. Therefore, in this paper we study the cone-adapted shearlet system to cover
whole \(\mathbb{R}^2\) and for giving equal treatment of all directions. Since the horizontal and vertical cones are treated
similarly by just interchanging \(w_1\) and \(w_2,w = (w_1;w_2) \in \mathbb{R}^2\), we study only horizontal cone and derived
some basic results concerning to continuous shearlet transform.
262
269
Devendra
Kumar
Department of Mathematics, Faculty of Science
Al-Baha University
Saudi Arabia, KSA
d_kumar001@rediffmail.com
Shiv
Kumar
Department of Mathematics
Research Scholar
D. A. V. College
I.K. Gujral Punjab Technical University
India
India
abhituli60@gmail.com
Balbir
Singh
College of Management and Technology
India
drbalbirdhami@yahoo.com
Shearlets
continuous shearlet transform
cone-adapted shearlet system
Parseval formula.
Article.25.pdf
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[1]
E. J. Candés, D. L. Donoho, Ridgelets: The key to high dimensional intermittency, Philos Trans. Roy. Soc. Lond. Ser., 357 (1999), 2495-2509
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PPF dependent fixed point in modified Razumikhin class with applications
PPF dependent fixed point in modified Razumikhin class with applications
en
en
In this paper we introduce the concepts of \(c-C_{\alpha\beta}-\)admissible mapping, \((\alpha\beta)_c-\Theta-\)contraction, weak
\((\alpha\beta)_c-\Theta-\)contraction, generalized \((\alpha\beta)_c-\Theta-\)contraction and establish the existence of PPF dependent fixed
point theorems for such classes of contractive nonself-mappings in the Razumikhin class. We give, also, a
result of existence of a PPF dependent fixed point by a condition of Suzuki type. As applications of our
theorems, we deduce some PPF dependent fixed point theorems for nonself-mappings valued in a Banach
space endowed with a graph or a partial order, and furnish an illustrative example to support our main
theorem.
270
286
M.
Paknazar
Department of Mathematics
Farhangian University
Iran
m.paknazar@cfu.ac.ir
M. A.
Kutbi
Department of Mathematics
King Abdulaziz University
Saudi Arabia
mkutbi@yahoo.com
M.
Demma
Università degli Studi di Palermo
Italy
martanoir91@hotmail.it
P.
Salimi
Young Researchers and Elite Club
Islamic Azad University--Rasht Branch
Iran
salimipeyman@gmail.com
Razumikhin class
PPF dependent fixed point
\((\alpha\beta)_c-\Theta-\)contraction
generalized \((\alpha\beta)_c-\Theta-\)contraction.
Article.26.pdf
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[1]
M. Abbas, T. Nazir , Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph, Fixed Point Theoery Appl., 2013 (2013), 1-8
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R. P. Agarwal, P. Kumam, W. Sintunavarat , PPF dependent fixed point theorems for an \(\alpha_c\)-admissible non-self mapping in the Razumikhin class, Fixed Point Theory Appl., 2013 (2013), 1-14
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A. G. B. Ahmad, Z. Fadail, H. K. Nashine, Z. Kadelburg, S. Radenović, Some new common fixed point results through generalized altering distances on partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-15
##[5]
S. R. Bernfeld, V. Lakshmikatham, Y. M. Reddy, Fixed point theorems of operators with PPF dependence in Banach spaces, Appl. Anal., 6 (1977), 271-280
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F. Bojor , Fixed point theorems for Reich type contraction on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901
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L. B. Ćirić, M. Abbas, R. Saadati, N. Hussain , Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., 217 (2011), 5784-5789
##[8]
L. B. Ćirić, S. M. Alsulami, P. Salimi, P. Vetro, PPF dependent fixed point results for triangular \(\alpha_c\)-admissible mappings, The Sci. World J., 2014 (2014), 1-10
##[9]
Y. J. Cho, Th. M. Rassias, P. Salimi, M. Turinici, Some PPF dependent fixed point theorems for new contractions in Banach spaces, Preprint, (2014)
##[10]
M. Cosentino, P. Salimi, P. Vetro, Fixed point results on metric-type spaces , Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 1237-1253
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B. C. Dhage, Some basic random fixed point theorems with PPF dependence and functional random differential equations, Differ. Equat. Appl., 4 (2012), 181-195
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N. Hussain, S. Al-Mezel, P. Salimi, Fixed points for \(\psi\)-graphic contractions with application to integral equations, Abstr. Appl. Anal., 2013 (2013), 1-11
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N. Hussain, S. Khaleghizadeh, P. Salimi, F. Akbar, New fixed point results with PPF dependence in Banach spaces endowed with a graph, Abstr. Appl. Anal., 2013 (2013), 1-9
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N. Hussain, A. R. Khan, R. P. Agarwal, Krasnosel'skii and Ky Fan type fixed point theorems in ordered Banach spaces, J. Nonlinear Convex Anal., 11 (2010), 475-489
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J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359-1373
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R. Johnsonbaugh, Discrete Mathematics , Prentice-Hall, Inc., New Jersey (1997)
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A. Kaewcharoen, PPF dependent common fixed point theorems for mappings in Bnach spaces, J. Inequal. Appl., 2013 (2013), 1-14
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F. Khojasteh, E. Karapinar, S. Radenović , \(\theta\)-metric spaces: A generalization, Math. Probl. Eng., 2013 (2013), 1-7
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M. Jleli, B Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
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P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 1-19
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B. Samet, C. Vetro, P. Vetro, Fixed point theorem for \(\alpha-\psi\) contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317
]
Computing center conditions for resonant infinity via integrating factor method
Computing center conditions for resonant infinity via integrating factor method
en
en
In this literature, the calculation of generalized center conditions is addressed for resonant infinity of a
polynomial vector field in \(\mathbb{C}^2\). The technique is taking resonant infinity into elementary resonant origin by
a homeomorphism. Afterwards, an algorithm to compute generalized singular point quantities is developed,
which is a good approach to find the necessary conditions of generalized center for any rational resonance
ratio. Finally, the necessary and sufficient conditions of generalized center for resonant infinity are obtained.
287
294
Yusen
Wu
School of Mathematics and Statistics
Henan University of Science and Technology
P. R. China
wuyusen621@126.com
Feng
Li
School of Science
Linyi University
P. R. China
lf0539@126.com
Generalized complex center
resonant infinity
integrating factor method.
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]
Coupled systems of Riemann-Liouville fractional differential equations with Hadamard fractional integral boundary conditions
Coupled systems of Riemann-Liouville fractional differential equations with Hadamard fractional integral boundary conditions
en
en
In this paper we study existence and uniqueness of solutions for coupled systems consisting from fractional
differential equations of Riemann-Liouville type subject to coupled and uncoupled Hadamard fractional
integral boundary conditions. The existence and uniqueness of solutions is established by Banach's contraction principle, while the existence of solutions is derived by using Leray-Schauder's alternative. Examples
illustrating our results are also presented.
295
308
Jessada
Tariboon
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Thailand
jessada.t@sci.kmutnb.ac.th
Sotiris K.
Ntouyas
Department of Mathematics
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
University of Ioannina
King Abdulaziz University
Greece
Saudi Arabia
sntouyas@uoi.gr
Weerawat
Sudsutad
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Thailand
wrw.sst@gmail.com
Riemann-Liouville fractional derivative
Hadamard fractional integral
coupled system
existence
uniqueness
fixed point theorems.
Article.28.pdf
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[1]
R. P. Agarwal, Y. Zhou, Y. He, Existence of fractional neutral functional differential equations , Comput. Math. Appl., 59 (2010), 1095-1100
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B. Ahmad, J. J. Nieto, Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Bound. Value Probl., 2011 (2011), 1-9
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B. Ahmad, J. J. Nieto, Boundary value problems for a class of sequential integrodifferential equations of fractional order, J. Funct. Spaces Appl., 2013 (2013), 1-8
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B. Ahmad, S. K. Ntouyas, A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions , Adv. Difference Equ., 2011 (2011), 1-11
##[5]
B. Ahmad, S. K. Ntouyas, A. Alsaedi, A study of nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type multistrip boundary conditions, Math. Probl. Eng.,, 2013 (2013), 1-9
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X. Liu, M. Jia, W. Ge , Multiple solutions of a p-Laplacian model involving a fractional derivative , Adv. Difference Equ., 2013 (2013), 1-12
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D. O'Regan, S. Stanek , Fractional boundary value problems with singularities in space variables, Nonlinear Dynam., 71 (2013), 641-652
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I. Podlubny , Fractional Differential Equations, Academic Press, San Diego (1999)
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J. Tariboon, S. K. Ntouyas, W. Sudsutad, Positive solutions for fractional differential equations with three-point multi-term fractional integral boundary conditions, Adv. Difference Equ., 2014 (2014), 1-17
##[20]
L. Zhang, B. Ahmad, G. Wang, R. P. Agarwal , Nonlinear fractional integro-differential equations on unbounded domains in a Banach space, J. Comput. Appl. Math., 249 (2013), 51-56
]
Computation and stability analysis of Hopf Bifurcation in biophysical system model of cells
Computation and stability analysis of Hopf Bifurcation in biophysical system model of cells
en
en
Dynamics of the Shen-Larter calcium oscillation model is investigated based on the theory of the center
manifold and bifurcation, including the classification and stability of equilibrium. The existence of two
subcritical Hopf bifurcations is derived in this case. More precisely, it is shown that the subcritical Hopf bi-furcations play a great role in the study of this calcium oscillation model. In addition, numerical simulations
are provided to verify our theoretical analysis and to display new phenomena. Based on the theoretical analysis results and the numerical results, an effective mechanism explaining the Shen-Larter calcium oscillation
model is obtained.
309
315
Yi
Zhou
School of Mathematical and Computational Science
Huainan Normal University
P. R. China
zhouyi3280@163.com
Calcium ion
Hopf
equilibrium.
Article.29.pdf
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]
A Time-varying repairable system with repairman vacation and warning device
A Time-varying repairable system with repairman vacation and warning device
en
en
In this paper, a new kind of repairable system with repairman vacation and warning device is discussed,
in which the delayed vacation rate and failure rates are functions related to system working time. The
system model is established by using probability analysis method, which then is translated into a initial
value problem of a class of abstract semi-linear evolution equation in a suitable Banach space for further
study. The conditions of the existence and uniqueness of the system solution as well as system stability is
analyzed by using \(C_0\)-semigroup theory. Some steady-state reliability indexes are studied by using Laplace
transformation. In the end, numerical examples are presented to compare some indexes of the systems with
and without warning device.
316
331
Lina
Guo
Department of Mathematics
Taiyuan University of Technology
P. R. China
guolina982@163.com
Maomao
Zhang
Department of Mathematics
Taiyuan University of Technology
P. R. China
sxdtdxzmm@126.com
Repairable system
delayed-multiple vacations
semi-linear evolution system
\(C_0\)-semigroup theory
well-posedness
stability
sensitivity analysis.
Article.30.pdf
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[1]
J. H. Cao, K. Cheng, Introduction to reliability mathematics, Higher Education Press, Beijing (1986)
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B. T. Doshi , Queueing system with vacations-a survey, Queueing Systems Theory Appl., 1 (1986), 29-66
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M. Jain, Rakhee, M. Singh, Bilevel control of degraded machining system with warm standbys, setup and vacation, Appl. Math. Model., 28 (2004), 1015-1026
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J. C. Ke, K. H. Wang , Vacation policies for machine repair problem with two type spares, Appl. Math. Model., 31 (2007), 880-894
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J. C. Ke, C. H. Wu, Z. G. Zhang , Recent developments in vacation models: a short survey, Int. J. Oper. Res., 7 (2010), 3-8
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R. B. Liu, Y. H. Tang, Reliability analysis of a two-dissimilar-unit cold standby system with separated repair rule, J. Syst. Eng., 21 (2006), 628-635
##[12]
R. B. Liu, Y. H. Tang , One-unit repairable system with multiple delay vacations, Gongcheng Shuxue Xuebao, 23 (2006), 721-724
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R. B. Liu, Y. H. Tang, C. Y. Luo , A new kind of N-unit series repairable system and its reliability analysis, Math. Appl., 20 (2007), 164-170
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]
On the Ulam stability of an n-dimensional quadratic functional equation
On the Ulam stability of an n-dimensional quadratic functional equation
en
en
In the present paper, we construct a new n-dimensional quadratic functional equation with constant coefficients
\[\sum^n_{i,j=1}f(x_i+x_j)=2\sum^n_{1\leq i< j\leq n}f(x_i-x_j)+4f\left(\sum^n_{i=1}x_i\right)\]
And then, we study the Ulam stability of the preceding equation in a real normed space and a non-
Archimedean space, respectively.
332
341
Yonghong
Shen
School of Mathematics and Statistics
School of Mathematics and Statistics
Tianshui Normal University
Beijing Institute of Technology
P. R. China
P. R. China
shenyonghong2008@hotmail.com
Wei
Chen
School of Information
Capital University of Economics and Business
P. R. China
chenwei@cueb.edu.cn
Ulam stability
n-dimensional quadratic functional equation
normed space
non-Archimedean space.
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J. H. Bae, K. W. Jun , On the generalized Hyers-Ulam-Rassias stability of an n-dimensional quadratic functional equation , J. Math. Anal. Appl., 258 (2001), 183-193
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P. Nakmahachalasint , On the generalized Ulam-Gavruta-Rassias stability of mixed-type linear and Euler-Lagrange-Rassias functional equations, Intern. J. Math. and Math. Sciences, 2007 (2007), 1-10
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C. Park, H. A. Kenary, T. M. Rassias, Hyers-Ulam-Rassias stability of the additive-quadratic mappings in non-Archimedean Banach spaces, J. Inequal. Appl., 2012 (2012), 1-18
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]
Existence of viscosity solutions with asymptotic behavior of exterior problems for Hessian equations
Existence of viscosity solutions with asymptotic behavior of exterior problems for Hessian equations
en
en
The Perron method is used to establish the existence of viscosity solutions of exterior problems for a class
of Hessian type equations with prescribed behavior at infinity.
342
349
Xianyu
Meng
Department of Mathematics
Harbin Institute of Technology
P. R. China
mcauchy@163.com
Yongqiang
Fu
Department of Mathematics
Harbin Institute of Technology
P. R. China
fuyongqiang@hit.edu.cn
Hessian equation
viscosity solution
asymptotic behavior
exterior problem coincidence.
Article.32.pdf
[
[1]
L. Caffarelli, Y. Y. Li , An extension to a theorem of Jörgens, Calabi and Pogorelov , Comm. Pure Appl. Math., 56 (2003), 549-583
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