]>
2018
11
4
ISSN 2008-1898
146
Some reverse Hölder inequalities with Specht's ratio on time scales
Some reverse Hölder inequalities with Specht's ratio on time scales
en
en
In this article, we investigate some new reverse Hölder-type inequalities
on an arbitrary time scale via the diamond-\(\alpha\) dynamic integral, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues.
444
455
A. A.
El-Deeb
Department of Mathematics, Faculty of Science
Al-Azhar University
Egypt
ahmedeldeeb@azhar.edu.eg
H. A.
Elsennary
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Engineering
Al-Azhar University
Sinai University
Egypt
Egypt
hamza.abderabou@su.edu.eg
Wing-Sum
Cheung
Department of Mathematics
The University of Hong Kong
wscheung@hku.hk
Dynamic inequalities of Hölder type
analysis techniques
time scales
Specht's ratio
Article.1.pdf
[
[1]
S. Abramovich, B. Mond, J. E. Pečarić , Sharpening Hölder’s Inequality , J. Math. Anal. Appl., 196 (1995), 1131-1134
##[2]
R. Agarwal, M. Bohner, A. Peterson , Inequalities on time scales: a survey , Math. Inequal. Appl., 4 (2001), 535-557
##[3]
R. P. Agarwal, D. O’Regan, S. Saker , Dynamic inequalities on time scales, Springer, Cham (2014)
##[4]
J. M. Aldaz , A stability version of Hölder’s inequality, J. Math. Anal. Appl., 343 (2008), 842-852
##[5]
E. F. Beckenbach, R. Bellman, Inequalities, Springer-Verlag, Berlin (1961)
##[6]
M. Bohner, A. Peterson , Dynamic equations on time scales, Birkhäuser Boston, Inc., Boston (2001)
##[7]
M. Bohner, A. Peterson, Advances in dynamic equations on time scales, Birkhäuser Boston, Inc., Boston (2003)
##[8]
C. Borell, Inverse Hölder inequalities in one and several dimensions, J. Math. Anal. Appl., 41 (1973), 300-312
##[9]
J. I. Fujii, S. Izumino, Y. Seo , Determinant for positive operators and Spechts theorem , Sci. Math., 1 (1998), 307-310
##[10]
G. H. Hardy, J. E. Littlewood, G. Pólya , In-equalities , Cambridge university press, Cambridge (1952)
##[11]
S. Hilger , Analysis on measure chains–a unified approach to continuous and discrete calculus, Results Math., 18 (1990), 18-56
##[12]
V. Kac, P. Cheung , Quantum calculus, Springer-Verlag, New York (2002)
##[13]
Y.-I. Kim, X. Yang , Generalizations and refinements of Hölders inequality, Appl. Math. Lett., 25 (2012), 1094-1097
##[14]
E. G. Kwon, E. K. Bae , On a continuous form of Hölder inequality, J. Math. Anal. Appl., 343 (2008), 585-592
##[15]
D. S. Mitrinović , Analytic inequalities, In cooperation with P. M. Vasić, Springer-Verlag, New York-Berlin (1970)
##[16]
D. S. Mitrinović, J. Pečarić, A. M. Fink, Classical and new inequalities in analysis , Kluwer Academic Publishers Group, Dordrecht (1993)
##[17]
G. S. Mudholkar, M. Freimer, P. Subbaiah, An extension of Hölder inequality , J. Math. Anal. Appl., 102 (1984), 435-441
##[18]
H. Qiang, Z. Hu , Generalizations of Hölder’s and some related inequalities, Comput. Math. Appl., 61 (2011), 392-396
##[19]
Q. Sheng, M. Fadag, J. Henderson, J. M. Davis , An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Anal. Real World Appl., 7 (2006), 395-413
##[20]
W. Specht, Zur theorie der elementaren mittel , Math. Z, 74 (1960), 91-98
##[21]
J. Tian , Reversed version of a generalized sharp Hölder’s inequality and its applications, Inform. Sci., 201 (2012), 61-69
##[22]
M. Tominaga, Specht’s ratio in the Young inequality , Sci. Math. Jpn., 55 (2002), 583-588
##[23]
Y. V. Venkatesh, Converse Hölder inequality and the Lp-instability of non-linear time-varying feedback systems, Nonlinear Anal. Theor. Methods Appl., 12 (1988), 247-258
##[24]
L. Wu, J. Sun, X. Ye, L. Zhu , Hölder type inequality for Sugeno integral, Fuzzy Sets and Systems, 161 (2010), 2337-2347
##[25]
X. Yang , Hölder’s inequality , Appl. Math. Lett., 16 (2003), 897-903
##[26]
W. Yang , A functional generalization of diamond-\(\alpha\) integral Hölder’s inequality on time scales, Appl. Math. Lett., 23 (2010), 1208-1212
##[27]
C.-J. Zhao, W. S. Cheung , Hölder’s reverse inequality and its applications, Publ. Inst. Math., 99 (2016), 211-216
]
Stability of pathogen dynamics models with viral and cellular infections and immune impairment
Stability of pathogen dynamics models with viral and cellular infections and immune impairment
en
en
We study the global stability analysis of pathogen infection models with
immune impairment. Both pathogen-to-susceptible and infected-to-susceptible
transmissions have been considered. We drive the basic reproduction
parameter \(\mathcal{R}_{0}\), which determines the global dynamics of
models. Using the method of Lyapunov function, we established the global
stability of the steady states of the models. Numerical simulations are used
to confirm the theoretical results.
456
468
A. M.
Elaiw
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
a_m_elaiw@yahoo.com
A. A.
Raezah
Department of Mathematics, Faculty of Science
King Khalid University
Saudi Arabia
aalraezh@kku.edu.sa
B. S.
Alofi
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Global stability
pathogen infection
immune impairment transfer
Lyapunov function
cell-to-cell transmission
Article.2.pdf
[
[1]
R. A. Arnaout, M. A. Nowak, D. Wodarz , HIV1 dynamics revisited: biphasic decay by cytotoxic T lymphocyte killing?, Proc. Roy. Soc. Lond. B, 267 (2000), 1347-1354
##[2]
E. Avila-Vales, N. Chan-Chí, G. García-Almeida , Analysis of a viral infection model with immune impairment, intracellular delay and general non-linear incidence rate , Chaos Solitons Fractals, 69 (2014), 1-9
##[3]
D. S. Callaway, A. S. Perelson , HIV-1 infection and low steady state viral loads, Bull. Math. Biol., 64 (2002), 29-64
##[4]
S.-S. Chen, C.-Y. Cheng, Y. Takeuchi , Stability analysis in delayed within-host viral dynamics with both viral and cellular infections, J. Math. Anal. Appl., 442 (2016), 642-672
##[5]
R. V. Culshaw, S. Ruan, G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay, J. Math. Biol., 46 (2003), 425-444
##[6]
A. M. Elaiw , Global properties of a class of HIV models, Nonlinear Anal. Real World Appl., 11 (2010), 2253-2263
##[7]
A. M. Elaiw , Global dynamics of an HIV infection model with two classes of target cells and distributed delays , Discrete Dyn. Nat. Soc., 2012 (2012), 1-13
##[8]
A. M. Elaiw, Global properties of a class of virus infection models with multitarget cells, Nonlinear Dynam., 69 (2012), 423-435
##[9]
A. M. Elaiw, R. M. Abukwaik, E. O. Alzahrani , Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays, Int. J. Biomath., 2014 (2014), 1-25
##[10]
A. M. Elaiw, N. A. Almuallem, Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells , Math. Methods Appl. Sci., 39 (2016), 4-31
##[11]
A. M. Elaiw, N. H. AlShamrani , Global properties of nonlinear humoral immunity viral infection models, Int. J. Biomath., 2015 (2015), 1-53
##[12]
A. M. Elaiw, N. H. AlShamrani , Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Anal. Real World Appl., 26 (2015), 161-190
##[13]
A. M. Elaiw, S. A. Azoz, Global properties of a class of HIV infection models with Beddington-DeAngelis functional response , Math. Methods Appl. Sci., 36 (2013), 383-394
##[14]
A. M. Elaiw, I. Hassanien, S. A. Azoz , Global stability of HIV infection models with intracellular delays , J. Korean Math. Soc., 49 (2012), 779-794
##[15]
A. M. Elaiw, A. A. Raezah, K. Hattaf, Stability of HIV-1 infection with saturated virus-target and infected-target incidences and CTL immune response, Int. J. Biomath., 2017 (2017), 1-29
##[16]
H. Gómez-Acevedo, M. Y. Li, Backward bifurcation in a model for HTLV-I infection of CD4+ T cells, Bull. Math. Biol., 67 (2005), 101-114
##[17]
Z. Hu, J. Zhang, H. Wang, W. Ma, F. Liao, Dynamics analysis of a delayed viral infection model with logistic growth and immune impairment, Appl. Math. Model., 38 (2014), 524-534
##[18]
D. Huang, X. Zhang, Y. Guo, H.Wang, Analysis of an HIV infection model with treatments and delayed immune response , Appl. Math. Model., 40 (2016), 3081-3089
##[19]
P. Krishnapriya, M. Pitchaimani , Analysis of time delay in viral infection model with immune impairment, J. Appl. Math. Comput., 55 (2017), 421-453
##[20]
P. Krishnapriya, M. Pitchaimani, Modeling and bifurcation analysis of a viral infection with time delay and immune impairment, Jpn. J. Ind. Appl. Math., 34 (2017), 99-139
##[21]
X. Lai, X. Zou, Modelling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission , SIAM J. Appl. Math., 74 (2014), 898-917
##[22]
X. Lai, X. Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl., 426 (2015), 563-584
##[23]
B. Li, Y. Chen, X. Lu, S. Liu , A delayed HIV-1 model with virus waning term , Math. Biosci. Eng., 13 (2016), 135-157
##[24]
X. Li, S. Fu , Global stability of a virus dynamics model with intracellular delay and CTL immune response, Math. Methods Appl. Sci., 38 (2015), 420-430
##[25]
M. Y. Li, H. Shu , Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response, Nonlinear Anal. Real World Appl., 13 (2012), 1080-1092
##[26]
M. Y. Li, L. Wang , Backward bifurcation in a mathematical model for HIV infection in vivo with anti-retroviral treatment, Nonlinear Anal. Real World Appl., 17 (2014), 147-160
##[27]
C. Lv, L. Huang, Z. Yuan, Global stability for an HIV-1 infection model with Beddington–DeAngelis incidence rate and CTL immune response , Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 121-127
##[28]
C. Monica, M. Pitchaimani, Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intracellular delays, Nonlinear Anal. Real World Appl., 27 (2016), 55-69
##[29]
A. U. Neumann, N. P. Lam, H. Dahari, D. R. Gretch, T. E. Wiley, T. J. Layden, A. S. Perelson, Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy , Science, 282 (1998), 103-107
##[30]
M. A. Nowak, C. R. M. Bangham , Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79
##[31]
M. A. Nowak, R. May , Virus dynamics: Mathematical Principles of Immunology and Virology, Oxford Uni., UK (2000)
##[32]
J. Pang, J.-A. Cui , Analysis of a hepatitis B viral infection model with immune response delay , Int. J. Biomath., 2017 (2017), 1-18
##[33]
J. Pang, J.-A. Cui. J. Hui , The importance of immune responses in a model of hepatitis B virus , Nonlinear Dynam., 67 (2012), 723-734
##[34]
H. Pourbashash, S. S. Pilyugin, P. De Leenheer, C. McCluskey, Global analysis of within host virus models with cell-to-cell viral transmission, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 3341-3357
##[35]
R. R. Regoes, D. Wodarz, M. A. Nowak, Virus dynamics: the effect to target cell limitation and immune responses on virus evolution , J. Theor. Biol., 191 (1998), 451-462
##[36]
P. K. Roy, A. N. Chatterjee, D. Greenhalgh, Q. J. A. Khan, Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model, Nonlinear Anal. Real World Appl., 14 (2013), 1621-1633
##[37]
H. Shu, L.Wang, J.Watmough , Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses, SIAM J. Appl. Math., 73 (2013), 1280-1302
##[38]
X. Wang, A. M. Elaiw, X. Song , Global properties of a delayed HIV infection model with CTL immune response, Appl. Math. Comput., 218 (2012), 9405-9414
##[39]
K. Wang, A. Fan, A. Torres , Global properties of an improved hepatitis B virus model, Nonlinear Anal. Real World Appl., 11 (2010), 3131-3138
##[40]
J. Wang, M. Guo, X. Liu, Z. Zhao, Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Appl. Math. Comput., 291 (2016), 149-161
##[41]
J. Wang, J. Lang, X. Zou , Analysis of an age structured HIV infection model with virus-to-cell infection and cell-to-cell transmission , Nonlinear Anal. Real World Appl., 34 (2017), 75-96
##[42]
L. Wang, M. Y. Li, D. Kirschner, Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression , Math. Biosci., 179 (2002), 207-217
##[43]
S. Wang, X. Song, Z. Ge, Dynamics analysis of a delayed viral infection model with immune impairment , Appl. Math. Model., 35 (2011), 4877-4885
##[44]
K. Wang, W. Wang, X. Liu, Global Stability in a viral infection model with lytic and nonlytic immune response, Comput. Math. Appl., 51 (2006), 1593-1610
##[45]
Y. Yang, L. Zou, S. Ruan , Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions, Math. Biosci., 270 (2015), 183-191
##[46]
F. Zhang, J. Li, C. Zheng, L. Wang , Dynamics of an HBV/HCV infection model with intracellular delay and cell proliferation, Commun. Nonlinear Sci. Numer. Simul., 42 (2017), 464-476
##[47]
S. Zhang, X. Xu , Dynamic analysis and optimal control for a model of hepatitis C with treatment, Commun. Nonlinear Sci. Numer. Simul., 46 (2017), 14-25
##[48]
Y. Zhao, Z. Xu , Global dynamics for a delyed hepatitis C virus,infection model , Electron. J. Differential Equations, 2014 (2014), 1-18
]
Properties of hyperholomorphic functions and integrals for commutative-quaternionic valued functions
Properties of hyperholomorphic functions and integrals for commutative-quaternionic valued functions
en
en
We give representations and properties of a hyperholomorphic function with values in commutative-quaternions. We first consider expressions of commutative-quaternions. Also, we investigate the results of derivatives and integrations for a hyperholomorphic function of commutative-quaternionic variables in Clifford analysis.
469
476
Ji Eun
Kim
Department of Mathematics
Dongguk University
Republic of Korea
jeunkim@pusan.ac.kr
Hyperholomorphic function
commutative-quaternions
Cauchy-Riemann system
Clifford analysis
Article.3.pdf
[
[1]
P. Fjelstad, S. G. Gal , n-dimensional hyperbolic complex numbers, Adv. Appl. Clifford Algebras, 8 (1998), 47-68
##[2]
R. Fueter , Analytische funktionen einer quaternionenvariablen , Comment. Math. Helv., 4 (1932), 9-20
##[3]
J. D. Grant, I. A. B. Strachan , Hypercomplex Integrable Systems, Nonlinearity, 12 (1999), 1247-1261
##[4]
W. R. Hamilton, On quaternions; or on a new system of imaginaries in algebra , Lond. Edin. Dublin Phil. Mag. J. Sci., 25 (1944), 58-60
##[5]
] J. Kajiwara, Z. Li, K. H. Shon, Function spaces in complex and Clifford analysis, Hue University, Vietnam (2006)
##[6]
D. Kaledin , Integrability of the twistor space for a hypercomplex manifold, Selecta Math., 4 (1998), 271-278
##[7]
J. E. Kim, S. J. Lim, K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal., 2014 (2014), 1-8
##[8]
J. E. Kim, K. H. Shon, The Regularity of functions on Dual split quaternions in Clifford analysis, Abstr. Appl. Anal., 2014 (2014 ), 1-8
##[9]
J. E. Kim, K. H. Shon , Polar coordinate expression of hyperholomorphic functions on split quaternions in Clifford analysis, Adv. Appl. Clifford Algebr., 25 (2015), 915-924
##[10]
V. V. Kravchenkov, Applied Quaternion Analysis, Helderman, Berlin (2003)
##[11]
K. Nôno , Hyperholomorphic functions of a quaternion variable , Bull. Fukuoka Univ. Ed. III, 32 (1982), 21-37
##[12]
S. Olariu , Complex numbers in n dimensions , North-Holland Publishing Co., Amsterdam (2002)
##[13]
K. Scheicher, R. F. Tichy, K. W. Tomantschger , Elementary Inequalities in Hypercomplex Numbers , Anz. Österreich. Akad. Wiss. Math.-Natur. Kl., 134 (1997), 3-10
##[14]
A. Sudbery , Quaternionic Analysis, Math. Proc. Cambridge Philos. Soc., 85 (1979), 199-224
]
Dynamics of the fuzzy difference equation \(z_n =\max\{\frac{ 1}{ z_{n-m}} , \frac{\alpha_n }{z_{n-r} }\}\)
Dynamics of the fuzzy difference equation \(z_n =\max\{\frac{ 1}{ z_{n-m}} , \frac{\alpha_n }{z_{n-r} }\}\)
en
en
In this paper, we study the eventual periodicity of the following
fuzzy max-type difference equation
\[z_n=\max\{\frac{1}{z_{n-m}},\frac{\alpha_n}{z_{n-r}}\},\ \
n=0,1,\ldots,\] where \(\{\alpha_n\}_{n\geq 0}\) is a periodic
sequence of positive fuzzy numbers and the initial values
\(z_{-d},z_{-d+1},\ldots,z_{-1}\)
are positive fuzzy numbers with
\(d=\max\{m,r\}\). We show that if
\(\max(\mbox{supp}\ \alpha_n)<1\), then every positive solution of
this equation is eventually periodic with period \(2m\).
477
485
Taixiang
Sun
Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing
Guangxi Univresity of Finance and Economics
China
stxhql@gxu.edu.cn
Hongjian
Xi
Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing
Guangxi Univresity of Finance and Economics
China
x3009h@163.com
Guangwang
Su
Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing
Guangxi Univresity of Finance and Economics
China
s1g6w3@163.com
Bin
Qin
Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing
Guangxi Univresity of Finance and Economics
China
q3009b@163.com
Fuzzy max-type difference equation
positive solution
eventual periodicity
Article.4.pdf
[
[1]
K. A. Chrysafis, B. K. Papadopoulos, G. Papaschinopoulos , On the fuzzy difference equations of finance , Fuzzy Sets and Systems, 159 (2008), 3259-3270
##[2]
E. Hatir, T. Mansour, I. Yalçinkaya, On a fuzzy difference equation, Util. Math., 93 (2014), 135-151
##[3]
Q. He, C. Tao, T. Sun, X. Liu, D. Su, Periodicity of the positive solutions of a fuzzy max-difference equation, Abstr. Appl. Anal., 2014 (2014 ), 1-4
##[4]
R. Horčík, Solution of a system of linear equations with fuzzy numbers, Fuzzy Sets and Systems, 159 (2008), 1788-1810
##[5]
R. Kargar, T. Allahviranloo, M. Rostami-Malkhalifeh, G. R. Jahanshaloo, A proposed method for solving fuzzy system of linear equations, Sci. World J., 2014 (2014 ), 1-6
##[6]
G. J. Klir, B. Yuan , Fuzzy sets and fuzzy logic, Prentice-Hall PTR, New Jersey (1995)
##[7]
V. Lakshmikantham, A. S. Vatsala, Basic theory of fuzzy difference equations, J. Difference Equ. Appl., 8 (2002), 957-968
##[8]
H. T. Nguyen, E. A. Walker, A first course in fuzzy logic, CRC Press, Florida (1997)
##[9]
G. Papaschinopoulos, B. K. Papadopoulos , On the fuzzy difference equation \(x_{n+1} = A + x_n/x_{n-m}\), Fuzzy Sets and Systems, 129 (2002), 73-81
##[10]
G. Papaschinopoulos, B. K. Papadopoulos , On the fuzzy difference equation \(x_{n+1} = A + B/x_n\), Soft Comput., 6 (2002), 456-461
##[11]
G. Papaschinopoulos, G. Stefanidou, Boundedness and asymptotic behavior of the solutions of a fuzzy difference equation, Fuzzy Sets and Systems, 140 (2003), 523-539
##[12]
G. Stefanidou, G. Papaschinopoulos , A fuzzy difference equation of a rational form, J. Nonlinear Math. Phys., 12 (2005), 300-315
##[13]
G. Stefanidou, G. Papaschinopoulos , Behavior of the positive solutions of fuzzy max- difference equations, Adv. Difference Equ., 2005 (2005), 153-172
##[14]
G. Stefanidou, G. Papaschinopoulos , The periodic nature of the positive solutions of a nonlinear fuzzy max-difference equation, Inform. Sci., 176 (2006), 3694-3710
##[15]
G. Stefanidou, G. Papaschinopoulos, C. J. Schinas, On an exponential-type fuzzy difference equation, Adv. Difference Equ., 2010 (2010), 1-19
##[16]
C. Wu, B. Zhang, Embedding problem of noncompact fuzzy number space E~(I), Fuzzy Sets and Systems, 105 (1999), 165-169
##[17]
Q. H. Zhang, J. Liu , The first order fuzzy difference equation \(x_{n+1} = Ax_n + B\) , (Chinese), Mohu Xitong yu Shuxue, 23 (2009), 74-79
##[18]
Q. H. Zhang, J. Liu, Z. Luo, Dynamical behavior of a third-order rational fuzzy difference equation, Adv. Difference Equ., 2015 (2015), 1-18
##[19]
Q. H. Zhang, L. Yang, D. Liao , On the fuzzy difference equation \(x_{n+1} = A + \sum^k_{i =0} B/x_{n-i }\), International J. Math. Comput. Phys. Elect. Comput. Eng., 5 (2011), 490-495
##[20]
Q. H. Zhang, L. Yang, D. Liao, Behavior of solutions to a fuzzy nonlinear difference equation, Iran J. Fuzzy Sys., 9 (2012), 1-12
##[21]
Q. H. Zhang, L. Yang, D. Liao , On first order fuzzy Ricatti difference equation, Inform. Sci., 270 (2014), 226-236
]
Hitting probabilities for non-convex lattice
Hitting probabilities for non-convex lattice
en
en
In this paper, we consider three lattices with cells represented in Figures 1,
3, and 5 and we determine the probability that a random segment of constant length
intersects a side of the lattice considered.
486
489
G.
Caristi
Department of Economics
University of Messina
Italy
gcaristi@unime.it
M.
Pettineo
Department of Mathematics
University of Palermo
Italy
maria.pettineo@unipa.it
A.
Puglisi
Department of Economics
University of Messina
Italy
puglisia@unime.it
Geometric probability
stochastic geometry
random sets
random convex sets and integral geometry
Article.5.pdf
[
[1]
D. Barilla, G. Caristi, A. Puglisi, M. Stoka, A Laplace type problem for two hexagonal lattices of Delone with obstacles, Appl. Math. Sci., 7 (2013), 4571-4581
##[2]
D. Barilla, G. Caristi, E. Saitta, M. Stoka, A Laplace type problem for lattice with cell composed by two quadrilaterals and one triangle, Appl. Math. Sci., 8 (2014), 789-804
##[3]
D. Barilla, G. Caristi, A. Puglisi, M. Stoka, Laplace Type Problems for a Triangular Lattice and Different Body Test, Appl. Math. Sci., 8 (2014), 5123-5131
##[4]
G. Caristi, A. Puglisi, E. Saitta, A Laplace type for an regular lattices with convex-concave cell and obstacles rhombus, Appl. Math. Sci., (), -
##[5]
G. Caristi, E. L. Sorte, M. Stoka, Laplace problems for regular lattices with three different types of obstacles, Appl. Math. Sci., 5 (2011), 2765-2773
##[6]
G. Caristi, M. Stoka, A Laplace type problem for a regular lattice of Dirichlet-Voronoi with different obstacles, Appl. Math. Sci., 5 (2011), 1493-1523
##[7]
G. Caristi, M. Stoka, A laplace type problem for lattice with axial symmetric and different obstacles type (I), Far East J. Math. Sci., 58 (2011), 99-118
##[8]
G. Caristi, M. Stoka, A Laplace type problem for lattice with axial symmetry and different type of obstacles (II), Far East J. Math. Sci. (FJMS), 64 (2012), 281-295
##[9]
A. Duma, M. Stoka, Problems of , Rend. Circ. Mat. Palermo (2) Suppl., 70 (2002), 237-256
##[10]
H. Poincaré, Calcul des probabilités, Les Grands Classiques Gauthier-Villars, Paris (1912)
##[11]
M. Stoka, Probabilités géométriques de type , Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 110 (1976), 53-59
]
On certain classes of bi-univalent functions related to \(m\)-fold symmetry
On certain classes of bi-univalent functions related to \(m\)-fold symmetry
en
en
In our present investigation, we introduce two new
subclasses \(S_{\Sigma _{m}}(\alpha ,\lambda ,\mu )\) and \(S_{\Sigma
_{m}}(\beta ,\lambda ,\mu )\) of analytic and \(m\)-fold symmetric bi-univalent
functions in the open unit disk \(E\). Results concerning coefficient estimates
for the functions of these classes are derived. Many interesting new and
already existing corollaries are also presented.
490
499
Saqib
Hussain
COMSATS Institute of Information Technology
Abbotabad
Pakistan
saqib_math@yahoo.com
Shahid
Khan
Department of Mathematics
Riphah International University Islamabad
Pakistan
shahidmath761@gmail.com
Muhammad Asad
Zaighum
Department of Mathematics
Riphah International University Islamabad
Pakistan
asadzaighum@gmail.com
Maslina
Darus
School of Mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia 43600
Malaysia
maslina@ukm.edu.my
\(m\)-Fold symmetry
bi-univalent functions
coefficient estimates
Article.6.pdf
[
[1]
R. M. Ali, S. K. Lee, V. Ravichandran, S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett., 25 (2012), 344-351
##[2]
Ş. Altinkaya, S. Yalçin , Coefficient bounds for certain subclasses of m-fold symmetric bi-univalentf Functions, J. Math., 2015 (2015 ), 1-5
##[3]
M. K. Aouf, R. M. El-Ashwah, A. M. Abd-Eltawab, New subclasses of bi-univalent functions involving Dziok-Srivastava operator, ISRN Math. Anal., 2013 (2013 ), 1-5
##[4]
D. A. Brannan, J. G. Clunie, Aspects of Contemporary Complex Analysis, Academic Press, New York (1980)
##[5]
D. A. Brannan, T. S. Taha , On some classes of bi-univalent functions, Studia Univ. Babe-Bolyai Math., 31 (1986), 70-77
##[6]
S. Bulut , Coefficient estimates for initial Taylor-Maclaurin coefficients for a subclass of analytic and bi-univalent functions defined by Al-Oboudi differential operator , Sci. World J., 2013 (2013 ), 1-6
##[7]
S. Bulut, Coefficient estimates for new subclasses of analytic and bi-univalent functions defined by Al-Oboudi differential operator, J. Funct. Spaces Appl., 2013 (2013 ), 1-7
##[8]
S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math., 43 (2013), 59-65
##[9]
S. Bulut , Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions , Turk. J. Math., 40 (2016), 1386-1397
##[10]
S. Bulut , Coefficient estimates for a new subclass of analytic and bi-univalent functions , An. Ştiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 62 (2016), 305-311
##[11]
M. Çağlar, H. Orhan, N. Yağmur , Coefficient bounds for new subclasses of bi-univalent functions, Filomat, 27 (2013), 1165-1171
##[12]
E. Deniz , Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal., 2 (2013), 49-60
##[13]
E. Deniz, M. Çağlar, H. Orhan , Second Hankel determinant for bi-starlike and bi-convex functions of order \(\beta\),, Appl. Math. Comput., 271 (2015), 301-307
##[14]
P. L. Duren , Univalent Functions , Springer-Verlag , New York (1983)
##[15]
B. A. Frasin, M. K. Aouf, New subclasses of bi-univalent functions , Appl. Math. Lett., 24 (2011), 1569-1573
##[16]
S. P. Goyal, P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc., 20 (2012), 179-182
##[17]
S. G. Hamidi, J. M. Jahangiri, Unpredictably of the coefficients of m-fold symmetric bi-Starlike functions, Inter. J. Math., 2014 (2014 ), 1-8
##[18]
T. Hayami, S. Owa, Coefficient bounds for bi-univalent functions, PanAmer. Math. J., 22 (2012), 15-26
##[19]
W. Koepf, Coefficient of symmetric functions of bounded boundary rotations , Proc. Amer. Math. Soc., 105 (1989), 324-329
##[20]
M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), 63-68
##[21]
G. Murugusundaramoorthy, N. Magesh, V. Prameela , Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal., 2013 (2013 ), 1-3
##[22]
E. Netanyahu , The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in \(|z|<1\),, Arch. Ration. Mech. Anal., 32 (1969), 100-112
##[23]
C. Pommerenke , Univalent Functions, Vandenhoeck & Ruprecht, Göttingen (1975)
##[24]
S. Porwal, M. Darus, On a new subclass of bi-univalent functions, J. Egyptian Math. Soc., 21 (2013), 190-193
##[25]
H. M. Srivastava, S. Bulut, M. Çağlar, N. Yağmur, Coefficient estimates for a general subclass of analytic and bi- univalent functions, Filomat, 27 (2013), 831-842
##[26]
H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), 1188-1192
##[27]
H. M. Srivastava, S. Sivasubramanian, R. Sivakumar, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J., 7 (2014), 1-10
##[28]
S. Sümer Eker, Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions, Turkish J. Math., 40 (2016), 641-646
##[29]
T. S. Taha, Topics in univalent function theory , Ph.D. thesis, University of London, UK (1981)
##[30]
Q.-H. Xu, Y.-C. Gui, H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25 (2012), 990-994
##[31]
Q.-H. Xu, H.-G. Xiao, H. M. Srivastava , A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput., 218 (2012), 11461-11465
]
Fourier series of finite product of Bernoulli and ordered Bell functions
Fourier series of finite product of Bernoulli and ordered Bell functions
en
en
In this paper, we consider three types of functions given by products of Bernoulli and ordered Bell functions and derive their Fourier series expansions. In addition, we will express each of them in terms of Bernoulli functions.
500
515
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Dmitry V.
Dolgy
Hanrimwon
Kwangwoon University
Republic of Korea
dvdolgy@gmail.com
Jongkyum
Kwon
Department of Mathematics Education and ERI
Gyeongsang National University
Republic of Korea
mathkjk26@gnu.ac.kr
Fourier series
Bernoulli functions
ordered Bell functions
Article.7.pdf
[
[1]
M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with formulas, graphs, and mathematical tables , National Bureau of Standards Applied Mathematics Series, Government Printing Office, Washington, D.C. (1964)
##[2]
R. P. Agarwal, D. S. Kim, T. Kim, J. Kwon , Sums of finite products of Bernoulli functions, Adv. Difference Equ., 2017 (2017), 1-15
##[3]
D. V. Dolgy, D. S. Kim, T. Kim, T. Mansour, Sums of finite products of ordered Bell functions, , (preprint), -
##[4]
G. V. Dunne, C. Schubert , Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys., 7 (2013), 225-249
##[5]
C. Faber, R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math., 139 (2000), 173-199
##[6]
S. Gaboury, R. Tremblay, B.-J. Fugére, Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchi polynomials, Proc. Jangjeon Math. Soc., 17 (2014), 115-123
##[7]
G.-W. Jang, T. Kim, D. S. Kim, T. Mansour, Fourier series of functions related to Bernoulli polynomials, Adv. Stud. Contemp. Math., 27 (2017), 49-62
##[8]
T. Kim, Some identities for the Bernoulli, the Euler and Genocchi numbers and polynomials, Adv. Stud. Contemp. Math., 20 (2010), 23-28
##[9]
D. S. Kim, T. Kim , Bernoulli basis and the product of several Bernoulli polynomials, Int. J. Math. Math. Sci., 2012 (2012), 1-12
##[10]
D. S. Kim, T. Kim, A note on higher-order Bernoulli polynomials, J. Inequal. Appl., 2013 (2013), 1-9
##[11]
D. S. Kim, T. Kim,, Identities arising from higher-order Daehee polynomial bases, Open Math., 13 (2015), 196-208
##[12]
T. Kim, D. S. Kim, D. V. Dolgy, J.-W. Park , Fourier series of sums of products of ordered Bell and poly-Bernoulli functions, J. Inequal. Appl., 2017 (2017 ), 1-17
##[13]
T. Kim, D. S. Kim, G.-W. Jang, J. Kwon , Fourier series of sums of products of Genocchi functions and their applications, J. Nonlinear Sci. Appl., 10 (2017), 1683-1694
##[14]
T. Kim, D. S. Kim, S.-H. Rim, D. Dolgy , Fourier series of higher-order Bernoulli functions and their applications, J. Inequal. Appl., 2017 (2017 ), 1-8
##[15]
H. Liu, W. Wang, Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums, Discrete Math., 309 (2009), 3346-3363
##[16]
J. E. Marsden, Elementary classical analysis , W. H. Freeman and Company, San Francisco (1974)
##[17]
H. Miki, A relation between Bernoulli numbers, J. Number Theory, 10 (1978), 297-302
##[18]
H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci., 5 (2011), 390-444
]
Viral dynamics of an HIV model with pulse antiretroviral therapy and adherence
Viral dynamics of an HIV model with pulse antiretroviral therapy and adherence
en
en
An immunological model of HIV-1 infection that accounts for
antiretroviral drug uptake via explicit compartments is considered.
Different from traditional methods where the drug effects is
modeled implicitly as a proportional inhibition of viral infection
and production, in this paper, it is assumed that the CD4\(^+\) T
cells can 'prey on' the antiretroviral drugs and become the cells
which cannot be infected or produce new virions. Drug dymamics is
modeled applying impulsive differential equations. The basic
reproductive number \(R_0\) is defined via the next infection
operator. It is shown that with perfect adherence the virus can be
eradicated permanently if \(R_0\) is less than unity, otherwise, the
virus can persist by applying persistent theory. The effects of
imperfect adherence are also explored. The results indicate that
even for the same degree of adherence, different adherence patterns
may lead to different therapy outcomes. In particular, for regular
dosage missing, the more dosages are consecutively missed, the worse
therapy outcomes will be.
516
528
Youping
Yang
School of Mathematics and Statistics
Shandong Normal University
P. R. China
yyang@sdnu.edu.cn
Impulsive therapy
imperfect adherence
basic reproductive number
adherence pattern
Article.8.pdf
[
[1]
N. Bacaër, S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality, Morocco. J. Math. Biol., 53 (2006), 421-436
##[2]
D. Baĭnov, P. Simeonov, Impulsive differential equations: periodic solutions and applications, Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York (1993)
##[3]
S. Bonhoeffer, M. A. Nowak , Pre-existence and emergence of drug resistance in HIV-1 infection, Proc. R. Soc. Lond. B, 264 (1997), 631-637
##[4]
A. A. Ding, H. Wu, Assessing antiviral potency of anti-HIV therapies in vivo by comparing viral decay rates in viral dynamic models , Biostatistics, 2 (2001), 13-29
##[5]
N. M. Ferguson, C. A. Donnelly, J. Hooper, A. C. Ghani, C. Fraser, L. M. Bartley, R. A. Rode, P. Vernazza, D. Lapins, S. L. Mayer, R. M. Anderson, Adherence to antiretroviral therapy and its impact on clinical outcome in HIVinfected patients, J. R. Soc. Interface., 2 (2005), 349-363
##[6]
G. H. Friedland, A. Williams, , Attaining higher goals in HIV treatment: the central importance of adherence, AIDS, 13 (1999), 61-72
##[7]
Y. Huang, D. Liu, H. Wu, Hierarchical Bayesian methods for estimation of parameters in longitudinal HIV dynamic system, Biometrics, 62 (2006), 413-423
##[8]
Y. Huang, S. L. Rosenkranz, H. Wu , Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity, Math. Biosci., 184 (2003), 165-186
##[9]
O. Krakovska, L. M. Wahl , Optimal drug treatment regimens for HIV depend on adherence, J. Theoret. Biol., 246 (2007), 499-509
##[10]
V. Lakshmikantham, D. D. Baĭnov, P. S. Simeonov, Theory of impulsive differential equations, World Scientific Publishing Co., Inc., Teaneck, New Jersey (1989)
##[11]
L. Liu, X.-Q. Zhao, Y. Zhou , A Tuberculosis Model with Seasonality, Bull. Math. Biol., 72 (2010), 931-952
##[12]
J. Lou, R. J. Smith , Modelling the effects of adherence to the HIV fusion inhibitor enfuvirtide, J. Theoret. Biol., 268 (2011), 1-13
##[13]
J. M. McCune , The dynamics of \(CD4^+\) T-cell depletion in HIV disease, Nature, 410 (2001), 974-979
##[14]
A. R. McLean, M. A. Nowak , Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV, AIDS, 6 (1992), 71-79
##[15]
R. E. Miron, R. J. Smith, Modelling imperfect adherence to HIV induction therapy , BMC Infect. Dis., 2010 (2010), 1-16
##[16]
M. A. Nowak, S. Bonhoeffer, G. M. Shaw, R. M. May , Anti-viral drug treatment: dynamics of resistance in free virus and infected cell populations, J. Theor. Biol., 184 (1997), 203-217
##[17]
A. S. Perelson, P. W. Nelson , Mathematical analysis of HIV-1 dynamics in vivo , SIAM Rev., 41 (1999), 3-44
##[18]
A. N. Philips, M. Youlem, M. Johnson, C. Loveday, Use of stochastic model to develop understanding of the impact of different patterns of antiretroviral drug use on resistance development , AIDS, 15 (2001), 2211-2220
##[19]
L. Rong, Z. Feng, A. S. Perelson , Emergence of HIV-1 Drug Resistance During Antiretroviral Treatment , Bull. Math. Biol., 69 (2007), 2027-2060
##[20]
H. L. Smith , Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems , Mathematical Surveys and Monographs , American Mathematical Society, Providence (1995)
##[21]
R. J. Smith, Adherence to antiretroviral HIV drugs: how many doses can you miss before resistance emerges, Proc. R. Soc. B., 273 (2006), 617-624
##[22]
R. J. Smith, Explicitly accounting for antiretroviral drug uptake in theoretical HIV models predicts long-term failure of protease-only therapy , J. Theoret. Biol., 251 (2008), 227-237
##[23]
R. J. Smith, L. M. Wahl , Distinct effects of protease and reverse transcriptase inhibition in an immunological model of HIV-1 infection with impulsive drug effects, Bull. Math. Biol., 66 (2004), 1259-1283
##[24]
R. J. Smith, L. M. Wahl, Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects, Bull. Math. Biol., 67 (2005), 783-813
##[25]
E. Tchetgen, E. H. Kaplan, G. H. Friedland, , Public health consequences of screening patients for adherence to highly active antiretroviral therapy, JAIDS, 26 (2001), 119-129
##[26]
P. Van den Driessche, J.Watmough, Reproductive numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48
##[27]
L. M. Wahl, M. A. Nowak, Adherence and drug resistance: predictions for therapy outcome, Proc. R. Soc. London B., 267 (2000), 835-843
##[28]
W. Wang, X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dynam. Differential Equations, 20 (2008), 699-717
##[29]
Y. Xiao, A semi-stochastic model for HIV population Dynamics, Int. J. Biomath., 2 (2009), 391-404
##[30]
Y. Yang, Y. Xiao , Threshold dynamics for an HIV model in periodic environments, J. Math. Anal. Appl., 361 (2010), 59-68
##[31]
Y. Yang, Y. Xiao, The effects of population dispersal and pulse vaccination on disease control, Math. Comput. Modelling, 52 (2010), 1591-1604
##[32]
F. Zhang, X.-Q. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516
##[33]
X.-Q. Zhao, Dynamical Systems in Population Biology , Springer-Verlag, New York (2003)
]
Strong convergence of a new iterative algorithm for fixed points of asymptotically nonexpansive mappings
Strong convergence of a new iterative algorithm for fixed points of asymptotically nonexpansive mappings
en
en
In this paper, we investigate a new iterative implicit algorithm for fixed points of asymptotically nonexpansive mapping in Hilbert spaces. We also prove its strong convergence theorem under certain assumptions imposed on the parameters and extend some well-known results. As an application, we apply our main result to \(\mu\)-inverse strongly monotone mapping.
529
540
Yuanheng
Wang
Department of Mathematics
Zhejiang Normal University
China
yhwang@zjnu.cn
Jialei
Feng
Department of Mathematics
Zhejiang Normal University
China
1397638728@qq.com
Asymptotically nonexpansive
strong convergence
\(\mu\)-inverse strongly monotone mapping
Hilbert space
Article.9.pdf
[
[1]
E. Blum, W. Oettli , From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145
##[2]
L.-C. Ceng, C.-Y. 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
##[3]
Q. Fan, Z. Yao , Strong convergence theorems for a nonexpansive mapping and its applications for solving the split feasibility problem, J. Nonlinear Sci. Appl., 10 (2017), 1470-1477
##[4]
S. D. Flåm, A. S. Antipin , Equilibrium programming using proximal-like algorithms, Math. Programming, 78 (1996), 29-41
##[5]
T.-H. Kim, H.-K. Xu , Strong convergence of modified Mann iterations , Nonlinear Anal., 61 (2005), 51-60
##[6]
G. López, V. Martín-Márquez, F. Wang, H.-K. Xu , Forward-backword splitting methods for accretive operators in Banach spaces, Abstr. Appl. Anal., 2012 (2012 ), 1-25
##[7]
J. Lou, L.-J. Zhang, Z. He, Viscosity approximation methods for asymptotically nonexpansive mappings, Appl. Math. Comput., 203 (2008), 171-177
##[8]
A. Moudafi , Viscosity approximation methods for fixed points problems, J. Math. Anal. Appl., 241 (2000), 46-55
##[9]
K. Nakajo, W. Takahashi , Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups , J. Math. Anal. Appl., 279 (2003), 372-379
##[10]
J.-W. Peng, J.-C. Yao , A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappings , Nonlinear Anal., 71 (2009), 6001-6010
##[11]
J.-W. Peng, J.-C. Yao, Strong convergence theorems of iterative scheme based on the extra gradient method for mixed equilibrium problems and fixed point problems, Math. Comput. Modelling, 49 (2009), 1816-1828
##[12]
X. Qin, Y. J. Cho, S. M. Kang, Viscosity approximation methods for generalized equlibrium problems and fixed point problems with applications , Nonlinear Anal., 72 (2010), 99-112
##[13]
Y. Song, R. Chen, H. Zhou , Viscosity approximation methods for nonexpansive mapping sequences in Banach spaces, Nonlinear Anal., 66 (2007), 1016-1024
##[14]
P. Sunthrayuth, P. Kumam, Viscosity approximation methods base on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces , Math. Comput. Modelling, 58 (2013), 1814-1828
##[15]
Y.-H.Wang, Y.-H. Xia , Strong convergence for asymptotical pseudocontractions with the demiclosedness principle in banach spaces , Fixed Point Theory Appl., 2012 (2012 ), 1-8
##[16]
H.-K. Xu , Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[17]
H.-K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl., 116 (2003), 659-678
##[18]
H.-K. Xu , Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[19]
H.-K. Xu, M. A. Aoghamdi, N. Shahzad , The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015 ), 1-12
##[20]
Q. Yan, G. Cai , Convergence analysis of modified viscosity implicit rules of asymptotically nonexpansive mappings in Hilbert spaces, Revista de la Real Academia de Ciencias Exactas, Fasicas y Naturales., Serie A. Matematicas (RACSAM), 2017 (2017 ), 1-16
##[21]
Y. Yao, Y.-C. Liou, R. Chen, Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces, Nonlinear Anal., 67 (2007), 3311-3317
##[22]
Y. Yao, Y.-C. Liou, S. M. Kang , Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method , Comput. Math. Appl., 59 (2010), 3472-3480
##[23]
Y. Yao, M. A. Noor, Y.-C. Liou, S. M. Kang, Some new algorithms for solving mixed equilibrium problems, Comput. Math. Appl., 60 (2010), 1351-1359
##[24]
Y. Yao, N. Shahzad, Y.-C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015 ), 1-15
]
On mixed complex intersection bodies
On mixed complex intersection bodies
en
en
In 2013, the mixed complex intersection bodies of
star bodies was introduced. Following this, in the paper, we
establish Aleksandrov-Fenchel and Brunn-Minkowski type
inequalities for the mixed complex intersection bodies, which in
special case yield some of the recent results.
541
549
Chang-Jian
Zhao
Department of Mathematics
China Jiliang University
P. R. China
chjzhao@163.com;chjzhao@aliyun.com
Dual Minkowski inequality
Dual Brunn-Minkowski inequality
Width-integrals
Affine surface area
Projection body
Article.10.pdf
[
[1]
H. Busemann, Volume in terms of concurrent cross-sections, Pacific J. Math., 3 (1953), 1-12
##[2]
S. Campi , Stability estimates for star bodies in terms of their intersection bodies, Mathematika, 45, 287–303. (1998)
##[3]
S. Campi , Convex intersection bodies in three and four dimensions, Mathematika, 46 (1999), 15-27
##[4]
H. Fallert, P. Goodey, W. Weil, Spherical projections and centrally symmetric sets, Adv. Math., 129 (1997), 301-322
##[5]
R. J. Gardner , A positive answer to the Busemann–Petty problem in three dimensions, Ann. of Math., 140 (1994), 435-447
##[6]
R. J. Gardner, Intersection bodies and the Busemann-Petty problem, Trans. Amer. Math. Soc., 342 (1994), 435-445
##[7]
R. J. Gardner , On the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies, Bull. Amer. Math. Soc., 30 (1994), 222-226
##[8]
R. J. Gardner, Geometric Tomography, Cambridge University Press, Cambridge (1995), -
##[9]
R. J. Gardner , The Brunn-Minkowski inequality, Bull. Amer. Math. Soc., 39 (2002), 355-405
##[10]
R. J. Gardner, A. Koldobsky, T. Schlumprecht, An analytic solution to the Busemann-Petty problem , C. R. Acad. Sci. Paris Sér. I Math., 328 (1999), 29-34
##[11]
R. J. Gardner, A. Koldobsky, T. Schlumprecht, An analytic solution to the Busemann-Petty problem on sections of convex bodies, Ann. of Math., 149 (1999), 691-703
##[12]
P. Goodey, E. Lutwak, W. Weil, Functional analytic characterizations of classes of convex bodies, Math. Z., 222 (1996), 363-381
##[13]
P. Goodey, W. Weil, Intersection bodies and ellipsoids, Mathematika, 42 (1995), 295-304
##[14]
E. Grinberg, G. Zhang, Convolutions, transforms, and convex bodies, Proc. London Math. Soc., 78 (1999), 77-115
##[15]
A. Koldobsky, Intersection bodies, positive definite distributions, and the Busemann-Petty problem, Amer. J. Math., 120 (1998), 827-840
##[16]
A. Koldobsky , Intersection bodies in \(R^4\) , Adv. Math., 136 (1998), 1-14
##[17]
A. Koldobsky, Second derivative test for intersection bodies, Adv. Math., 136 (1998), 15-25
##[18]
A. Koldobsky , A functional analytic approach to intersection bodies, Geom. Funct. Anal., 10 (2000), 1507-1526
##[19]
A. Koldobsky , Fourier Analysis in Convex Geometry, American Mathematical Society, Providence (2005)
##[20]
A. Koldobsky, G. Paouris, M. Zymonopoulou , Complex Intersection Bodies, J. Lond. Math. Soc., 88 (2013), 538-562
##[21]
M. Ludwig, Intersection bodies and valuations, Amer. J. Math., 128 (2006), 1409-1428
##[22]
E. Lutwak , Intersection bodies and dual mixed volumes , Adv. in Math., 71 (1988), 232-261
##[23]
M. Moszyńska, Quotient star bodies, intersection bodies, and star duality, J. Math. Anal. Appl., 232 (1999), 45-60
##[24]
W. Wang, R. He, J. Yuan, Mixed complex intersection bodies, Math. Inequal. Appl., 18 (2015), 419-428
##[25]
G. Zhang , A positive solution to the Busemann-Petty problem in \(R^4\) , Ann. of Math., 149 (1999), 535-543
##[26]
C.-J. Zhao , Extremal Problems in Convex Bodies Geometry , Dissertation for the Doctoral Degree at Shanghai Univ., Shanghai (2005)
##[27]
C.-J. Zhao, \(L_p\)-mixed intersection bodies , Sci. China, 51 (2008), 2172-2188
##[28]
C.-J. Zhao, On intersection and mixed intersection bodies, Geom. Dedicata, 141 (2009), 109-122
##[29]
C.-J. Zhao, G.-S. Leng , Brunn-Minkowski inequality for mixed projection bodies, J. Math. Anal. Appl., 301 (2005), 115-123
##[30]
C.-J. Zhao, G.-S. Leng, Inequalities for dual quermassintegrals of mixed intersection bodies, Proc. Indian Acad. Sci. Math. Sci., 115 (2005), 79-91
]
Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays
Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays
en
en
The problem of guaranteed cost control for exponential function projective synchronization (EFPS) for complex dynamical networks with mixed time-varying delays and hybrid uncertainties asymmetric coupling delays, composing of state coupling, time-varying delay coupling, and distributed time-varying delay coupling, is investigated. In this work, the uncertainties coupling configuration matrix need not be symmetric or irreducible. The guaranteed cost control for EFPS of delayed complex dynamical networks is considered via hybrid control with nonlinear and mixed linear feedback controls, including error linear term, time-varying delay error linear term, and distributed time-varying delay error linear term. Based on the construction of improved Lyapunov-Krasovskii functional with the technique of dealing with some integral terms, the new sufficient conditions for the existence of the optimal guaranteed cost control laws are presented in terms of linear matrix inequalities (LMIs). The obtained LMIs can be efficiently solved by standard convex optimization algorithms. Moreover, numerical examples are given to demonstrate the effectiveness of proposed guaranteed cost control for EFPS. The results in this article generalize and improve the corresponding results of the recent works.
550
574
Wajaree
Weera
Department of Mathematics
University of Pha Yao
Thailand
wajaree.we@up.ac.th
Thongchai
Botmart
Department of Mathematics
Khon Kaen University
Thailand
thongbo@kku.ac.th
Piyapong
Niamsup
Department of Mathematics, Faculty of Science
Chiang Mai University
Thailand
piyapong.n@cmu.ac.th
Narongsak
Yotha
Department of Applied Mathematics and Statistics
Rajamangala University of Technology Isan
Thailand
narongsak.yo@rmuti.ac.th
Guaranteed cost control
exponential function projective synchronization
complex dynamical networks
hybrid uncertainties asymmetric coupling
Article.11.pdf
[
[1]
A. Abdurahman, H. Jiang, Z. Teng , Function projective synchronization of impulsive neural networks with mixed timevarying delays , Nonlinear Dynam., 78 (2014), 2627-2638
##[2]
R. Albert, H. Jeong, A.-L. Barabási, Internet: Diameter of the World-Wide Web, Nature, 401 (1999), 130-131
##[3]
M. N. Alpaslan Palarkçi , Robust delay-dependent guaranteed cost controller design for uncertain neutral systems, Appl. Math. Comput., 215 (2009), 2936-2949
##[4]
T. Botmart, P. Niamsup, Exponential synchronization of complex dynamical network with mixed time-varying and hybrid coupling delays via Intermittent control , Adv. Difference Equ., 2014 (2014 ), 1-33
##[5]
S. Cai, X. Lei, Z. Liu , Outer synchronization between two hybrid-coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control, Complexity, 21 (2016), 593-605
##[6]
J. Cao, G. Chen, P. Li , Global synchronization in an array of delayed neural networks with hybrid coupling , IEEE Trans. Syst., Man, Cybern., 38 (2008), 488-498
##[7]
S. Chang, T. Peng , Adaptive guaranteed cost control of systems with uncertain parameters, IEEE Trans. Automatic Control, 17 (1972), 474-483
##[8]
W.-H. Chen, Z.-H. Guan, X. Lu , Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems, Automatica J. IFAC, 40 (2004), 1263-1268
##[9]
B. Cui, X. Lou, Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control, Chaos Solitons & Fractals, 39 (2009), 288-294
##[10]
H. Du , Function projective synchronization in complex dynamical networks with or without external disturbances via error feedback control, Neurocomputing, 173 (2016), 1443-1449
##[11]
H. Du, P. Shi, N. Lü, Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control, Nonlinear Anal. Real World Appl., 14 (2013), 1182-1190
##[12]
M. Faloutsos, P. Faloutsos, C. Faloutsos, On power-law relationships of the Internet topology , Comput. Commun. Rev., 29 (1999), 251-262
##[13]
K. Gu, V. L. Kharitonov, J. Chen, Stability of time-delay system , Birkhäuser Boston, Boston (2003)
##[14]
W. He, F. Qian, J. Cao, Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control, Neural Netw., 85 (2017), 1-9
##[15]
P. He, X.-L. Wang, Y. Li , Guaranteed cost synchronization of complex networks with uncertainties and time-varying delays, complexity, 21 (2015), 381-395
##[16]
H. Jeong, B. Tombor, R. Albert, Z. Oltvai, A.-L. Barabási, The large-scale organization of metabolic network, Nature, 407 (2000), 651-653
##[17]
T. H. Lee, D. H. Ji, J. H. Park, H. Y. Jung , Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology, Appl. Math. Comput., 219 (2012), 996-1010
##[18]
T. H. Lee, J. H. Park, D. H. Ji, O. M. Kwon, S. M. Lee, Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control , Appl. Math. Comput., 218 (2012), 6469-6481
##[19]
B. Li, Pinning adaptive hybrid synchronization of two general complex dynamical networks with mixed coupling , Appl. Math. Model., 40 (2016), 2983-2998
##[20]
S. Li, W. Tang, J. Zhang , Guaranteed cost control of synchronisation for uncertain complex delayed networks, Internat. J. Systems Sci., 43 (2012), 566-575
##[21]
C.-H. Lien , Delay-dependent and delay-independent guaranteed cost control for uncertain neutral systems with timevarying delays via LMI approach, Chaos, Solitons & Fractals, 33 (2007), 1017-1027
##[22]
J. Lu, D.W. C. Ho, J. Cao, Synchronization in an array of nonlinearly coupled chaotic neural networks with delay coupling, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 18 (2008), 3101-3111
##[23]
Y.-P. Luo, B.-F. Zhou, Guaranteed cost synchronization of complex network systems with delay, Asian J. Control, 17 (2015), 1274-1284
##[24]
T. Ma, J. Zhang, Y. Zhou, H. Wang, Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes, Neurocomputing, 164 (2015), 182-189
##[25]
P. Niamsup, T. Botmart, W. Weera, Modified function projective synchronization of complex dynamical networks with mixed time-varying and asymmetric coupling delays via new hybrid pinning adaptive control, Adv. Difference Equ., 2017 (2017), 1-31
##[26]
J. H. Park, K. Choi , Guaranteed cost control of nonlinear neutral systems via memory state feedback, Chaos, Solitons & Fractals, 24 (2005), 183-190
##[27]
J. H. Park, O. Kwon , On guaranteed cost control of neutral systems by retarded integral state feedback, Appl. Math. Comput., 165 (2005), 393-404
##[28]
G. Rajchakit , Delay-dependent optimal guaranteed cost control of stochastic neural networks with interval nondifferentiable time-varying delays, Adv. Difference Equ., 2013 (2013 ), 1-11
##[29]
R. Rakkiyappan, N. Sakthivel , Cluster synchronization for TS fuzzy complex networks using pinning control with probabilistic time-varying delays, Complexity, 21 (2015), 59-77
##[30]
K. Sivaranjani, R. Rakkiyappan , Pinning sampled-data synchronization of complex dynamical networks with Markovian jumping and mixed delays using multiple integral approach, Complexity, 21 (2016), 622-632
##[31]
L. Shi, H. Zhu, S. Zhong, K. Shi, J. Cheng , Function projective synchronization of complex networks with asymmetric coupling via adaptive and pinning feedback control, ISA Trans., 65 (2016), 81-87
##[32]
L. Shi, H. Zhu, S. Zhong, Y. Zeng, J. Cheng, Synchronization for time-varying complex networks based on control, J. Comput. Appl. Math., 301 (2016), 178-187
##[33]
Q. Song, J. Cao , On pinning synchronization of directed and undirected complex dynamical networks, IEEE Trans. Circuits Syst. I. Regul. Pap., 57 (2010), 672-680
##[34]
S. H. Strogatz , Exploring complex networks, Nature, 410 (2001), 268-276
##[35]
D. Wang, D. Liu, C. Mu, H. Ma , Decentralized guaranteed cost control of interconnected systems with uncertainties: A learning-based optimal control strategy, Neurocomputing, 214 (2016), 297-306
##[36]
S. Wassrman, K. Faust, Social Network Analysis, Cambridge University Press, Cambridge (1994)
##[37]
R. J. Williams, N. D. Martinez, Simple rules yield complex food webs, Nature, 404 (2000), 180-183
##[38]
Y. Wu, C. Li, Y. Wu, J. Kurths, Generalized synchronization between two different complex networks, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 349-355
##[39]
Y. Wu, C. Li, A. Yang, L. Song, Y. Wu, Pinning adaptive anti-synchronization between two general complex dynamical networks with non-delayed and delayed coupling, Appl. Math. Comput., 218 (2012), 7445-7452
##[40]
X. Wu, H. Lu, Generalized projective synchronization between two different general complex dynamical networks with delayed coupling, Phys. Lett. A, 374 (2010), 3932-3941
##[41]
C. Xie, Y. Xu, D. Tong, Synchronization of time varying delayed complex networks via impulsive control, Optik- International Journal for Light and Electron Optics, 125 (2014), 3781-3787
##[42]
Y. Yang, J. Cao, Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects , Nonlinear Anal. Real World Appl., 11 (2010), 1650-1659
##[43]
W. Yu, G. Chen, J. Lü, On pinning synchronization of complex dynamical networks, Automatica, 45 (2009), 429-435
##[44]
R. Zhang, Y. Yang, Z. Xu, M. Hu , Function projective synchronization in drive-c response dynamical network, Phys. Lett. A, 374 (2010), 3025-3038
##[45]
Y.-P. Zhao, P. He, H. Saberi Nik, J. Ren, Robust adaptive synchronization of uncertain complex networks with multiple time-varying coupled delays, Complexity, 20 (2015), 49-60
]
Fourier series of sums of products of \(r\)-derangement functions
Fourier series of sums of products of \(r\)-derangement functions
en
en
A derangement is a permutation that has no fixed point and the derangement number \(d_m\) is the number of fixed point-free permutations on an \(m\) element set. A generalization of the derangement numbers are the \(r\)-derangement numbers and their natural companions are the \(r\)-derangement polynomials.
In this paper we will study three types of sums of products of \(r\)-derangement functions and find Fourier series expansions of them. In addition, we will express them in terms of Bernoulli functions. As immediate corollaries to this, we will be able to express the corresponding three types of polynomials as linear combinations of Bernoulli polynomials.
575
590
Taekyun
Kim
Department of Mathematics
Kwangwoon University
S. Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Huck-In
Kwon
Department of Mathematics
Kwangwoon University
S. Korea
sura@kw.ac.kr
Lee-Chae
Jang
Graduate School of Education
Konkuk University
Republic of Korea
lcjang@konkuk.ac.kr
Fourier series
\(r\)-derangement polynomials
Bernoulli polynomials
Article.12.pdf
[
[1]
L. Carlitz , The number of derangements of a sequence with given specification, Fibonacci Quart., 16 (1978), 255-258
##[2]
R. J. Clarke, M. Sved, Derangements and Bell numbers , Math. Mag., 66 (1993), 299-303
##[3]
P. R. de Montmort , Essay d’analyse sur les jeux de hazard , (French) [Essay on the analysis of games of chance], Chelsea Publishing Co., New York (1980)
##[4]
M. Hassani , Derangements and applications , J. Integer Seq., 2003 (2003), 1-8
##[5]
T. Kim, D. S. Kim , Degenerate Laplace transform and degenerate gamma function , Russ. J. Math. Phys., 24 (2017), 241-248
##[6]
T. Kim, D. S. Kim, D. V. Dolgy, J. Kwon , Some identities of derangement numbers , Proc. Jangjeon Math. Soc., 21 (2018), 125-141
##[7]
D. S. Kim, T. Kim, H.-I. Kwon , Fourier series of r-derangement and higher-order derangement functions , Adv. Stud. Contemp. Math. (Kyungshang), 28 (2018), 1-11
##[8]
I. Mezö , A generalization of the derangement numbers, , (Powerpoint Slides), -
##[9]
C. Wang, P. Miska, I. Mezö , The r-derangement numbers , Discrete Math., 340 (2017), 1681-1692
]