]>
2015
8
2
ISSN 2008-1898
87
Some common fixed point theorems in dislocated metric spaces
Some common fixed point theorems in dislocated metric spaces
en
en
Our purpose in this paper is to establish some new common fixed point theorems for four self-mappings of
a dislocated metric space.
86
92
Samia
Bennani
Department of Mathematics and Informatics, Faculty of Sciences Ben M'sik
University Hassan II-Mohammédia
Morocco
Hicham
Bourijal
Department of Mathematics and Informatics, Faculty of Sciences Ben M'sik
University Hassan II-Mohammédia
Morocco
Soufiane
Mhanna
Department of Mathematics and Informatics, Faculty of Sciences Ben M'sik
University Hassan II-Mohammédia
Morocco
Driss El
Moutawakil
Laboratory of Applied Mathematics and Technology of Information and Communication, Faculty Polydisciplinary of Khouribga
Morocco
d.elmoutawakil@gmail.com
Fixed point
common fixed point
dislocated metric space
weak compatibility.
Article.1.pdf
[
[1]
P. Hitzler, A. K. Seda , Dislocated Topologies, J. Electrical Engineering, 51 (2000), 3-7
##[2]
P. Hitzler , Generalized metrices and topology in logic programming semantics, Ph. D. Thesis, National University of Ireland, (University College, Cork) (2001)
##[3]
D. Panthi, K. Jha, A common fixed point of weakly compatible mappings in dislocated metric space, Kathmandu University J. Sci., Engineering and Technology, 8 (2012), 25-30
##[4]
I. Rambhadra Sarma, P. Sumati Kumari, On dislocated metric spaces, Int. J. Math. Archive, 3 (2012), 72-77
]
New results of positive solutions for second-order nonlinear three-point integral boundary value problems
New results of positive solutions for second-order nonlinear three-point integral boundary value problems
en
en
In this paper, we investigate the existence of positive solutions for second-order nonlinear three-point integral
boundary value problems. By using the Leray-Schauder fixed point theorem, some sufficient conditions
for the existence of positive solutions are obtained, which improve the results of literature Tariboon and
Sitthiwirattham [J. Tariboon, T. Sitthiwirattham, Boundary Value Problems, 2010 (2010), 1-11].
93
98
Zhijian
Yao
Department of Mathematics and Physics
Anhui Jianzhu University
China
zhijianyao@126.com
Positive solution
nonlinear three-point integral boundary value problems
Leray-Schauder fixed point theorem.
Article.2.pdf
[
[1]
Z. J. Du, W. G. Ge, X. J. Lin, Existence of solutions for a class of third-order nonlinear boundary value problems, J. Math. Anal. Appl., 294 (2004), 104-112
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Y. Q. Feng, S. Y. Liu, Solvability of a third-order two-point boundary value problem, Appl. Math. Letters, 18 (2005), 1034-1040
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J. R. Graef, B. Yang, Positive solutions to a multi-point higher order boundary value problem, J. Math. Anal. Appl., 316 (2006), 409-421
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A. Granas, J. Dugundji , Fixed point theory, Springer-Verlag, New York (2003)
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C. P. Gupta, Solvability of three-point nonlinear boundary value problem for a second order ordinary differential equation, J. Math. Anal. Appl., 168 (1992), 540-551
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B. Liu, Positive solutions of a nonlinear four-point boundary value problem, Appl. Math. Comput., 155 (2004), 179-203
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J. Tariboon, T. Sitthiwirattham, Positive solutions of a nonlinear three-point integral boundary value problem, Boundary Value Problems, 2010 (2010), 1-11
##[11]
J. R. L. Webb, Positive solutions of some three-point boundary value problems via fixed point index theory, Nonlinear Anal., 47 (2001), 4319-4332
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Y. M. Zhou, Y. Xu, Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations, J. Math. Anal. Appl., 320 (2006), 578-590
]
Positive solutions for Caputo fractional differential equations involving integral boundary conditions
Positive solutions for Caputo fractional differential equations involving integral boundary conditions
en
en
In this work we study integral boundary value problem involving Caputo differentiation
\[
\begin{cases}
^c D^q_t u(t)= f(t,u(t)),\,\, 0<t<1,\\
\alpha u(0)-\beta u(1)=\int^1_0 h(t)u(t)dt, \gamma u'(0)-\delta u'(1)\int^1_0 g(t)u(t)dt,
\end{cases}
\]
where \(\alpha,\beta,\gamma,\delta\)
are constants with \(\alpha>\beta>0,\gamma>\delta>0, f\in C([0,1]\times \mathbb{R}^+,\mathbb{R}), g,h\in C([0,1],\mathbb{R}^+)\) and \( ^c D^q_t\)
is the standard Caputo fractional derivative of fractional order \(q(1 < q < 2)\). By using some fixed point
theorems we prove the existence of positive solutions.
99
109
Yong
Wang
School of Science
Jiangnan University
China
yongwangjn@163.com
Yang
Yang
School of Science
Jiangnan University
China
yynjnu@126.com
Caputo fractional boundary value problem
fixed point theorem
positive solution.
Article.3.pdf
[
[1]
B. Ahmad, S. Ntouyas, A. Alsaedi , Existence of solutions for fractional q-integro-difference inclusions with fractional q-integral boundary conditions, Advances in Difference Equations, 2014 (2014), 1-18
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A. Cabada, G. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions, J. Math. Anal. Appl., 389 (2012), 403-411
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J. Henderson, H. Thompson, Multiple symmetric positive solutions for second order boundary-value problems, Proc. Amer. Math. Soc., 128 (2000), 2373-2379
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M. Jia, X. Liu, Three nonnegative solutions for fractional differential equations with integral boundary conditions , Comput. Math. Appl., 62 (2011), 1405-1412
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M. Jia, X. Liu, Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions, Appl. Math. Comput., 232 (2014), 313-323
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M. Krasnoselskii,. Zabreiko , Geometrical methods of nonlinear analysis, Springer-verlag, New York (1984)
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A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science, Amsterdam, The Netherlands (2006)
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R. Leggett, R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana. Univ. Math. J., 28 (1979), 673-688
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I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering , vol. 198, Academic Press, San Diego, Calif, USA (1999)
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S. Samko, A. Kilbas, O. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon (1993)
##[11]
J. Tariboon, S. Ntouyas, W. Sudsutad , Positive solutions for fractional differential equations with three-point multi-term fractional integral boundary conditions, Advances in Difference Equations, 2014 (2014), 1-17
##[12]
S. Vong, Positive solutions of singular fractional differential equations with integral boundary conditions, Math. Comput. Modelling, 57 (2013), 1053-1059
##[13]
Z. Wei, C. Pang, Y. Ding , Positive solutions of singular Caputo fractional differential equations with integral boundary conditions , Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 3148-3160
##[14]
S. Westerlund , Dead Matter Has Memory, Physica Scripta., 43 (1991), 174-179
##[15]
X. Xu, D. Jiang, C. Yuan, Multiple positive solutions to singular positone and semipositone Dirichlet-type boundary value problems of nonlinear fractional differential equations, Nonlinear Anal., 74 (2011), 5685-5696
##[16]
W. Yang , Positive solutions for nonlinear Caputo fractional differential equations with integral boundary conditions , J. Appl. Math. Comput., 44 (2014), 39-59
##[17]
W. Yang , Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions, Appl. Math. Comput., 244 (2014), 702-725
##[18]
X. Zhang, Positive solution for a class of singular semipositone fractional differential equations with integral boundary conditions , Boundary Value Problems, 2012 (2012), 1-17
]
Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations
Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations
en
en
In this paper, we study the existence of positive solutions for a class of coupled integral boundary value
problems of nonlinear semipositone Hadamard fractional differential equations
\[D^\alpha u(t) + \lambda f(t, u(t), v(t)) = 0,\quad D^\alpha v(t) + \lambda g(t, u(t), v(t)) = 0,\quad t \in (1, e),\quad \lambda > 0\]
\[u^{(j)}(1) = v^{(j)}(1) = 0, 0 \leq j \leq n - 2; u(e) = \mu\int^e_1 v(s) \frac{ds}{ s} , v(e) = \nu\int^e_1 u(s) \frac{ds}{ s},\]
where \(\lambda,\mu,\nu\) are three parameters with \(0<\mu<\beta\) and \(0<\nu<\alpha,\quad \alpha,\beta\in (n - 1; n]\) are two real numbers
and \(n\geq 3, D^\alpha, D^\beta\) are the Hadamard fractional derivative of fractional order, and \(f; g\) are sign-changing
continuous functions and may be singular at \(t = 1\) or/and \(t = e\). First of all, we obtain the corresponding
Green's function for the boundary value problem and some of its properties. Furthermore, by means of the
nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorems, we derive an interval
of \(\lambda\) such that the semipositone boundary value problem has one or multiple positive solutions for any \(\lambda\)
lying in this interval. At last, several illustrative examples were given to illustrate the main results.
110
129
Wengui
Yang
Ministry of Public Education
Sanmenxia Polytechnic
China
wgyang0617@yahoo.com
Hadamard fractional differential equations
coupled integral boundary conditions
positive solutions
Green's function
fixed point theorems.
Article.4.pdf
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[1]
R. P. Agarwal, V. Lakshmikantham, J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonliear Anal., 72 (2010), 2859-2862
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R. P. Agarwal, M. Meehan, D. ORegan, Fixed Point Theory and Applications, Cambridge University Press, (2001)
##[3]
B. Ahmad, A. Alsaedi, Existence and uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations, Fixed Point Theory Appl., Art. ID 364560, 2010 (2010), 1-17
##[4]
B. Ahmad, J. Nieto, Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations, Abstr. Appl. Anal., Art. ID 494720, 2009 (2009), 1-9
##[5]
B. Ahmad, J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions , Comput. Math. Appl., 58 (2009), 1838-1843
##[6]
B. Ahmad, J. J. Nieto, Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Bound. Value Probl., 2011 (2011), 1-36
##[7]
B. Ahmad, S. K. Ntouyas, On Hadamard fractional integro-differential boundary value problems, J. Appl. Math. Comput., doi: 10.1007/s12190-014-0765-6. (2014)
##[8]
B. Ahmad, S. K. Ntouyas, A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 348-360
##[9]
B. Ahmad, S. K. Ntouyas , On three-point Hadamard-type fractional boundary value problems, Int. Electron. J. Pure Appl. Math., 8 (4) (2014), 31-42
##[10]
B. Ahmad, S. K. Ntouyas, A. Alsaedi, New results for boundary value problems of Hadamard-type fractional differential inclusions and integral boundary conditions, Bound. Value Probl., 2013 (2013), 1-275
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A. Anguraj, M. L. Maheswari, Existence of solutions for fractional impulsive neutral functional infinite delay integrodifferential equations with nonlocal conditions, J. Nonlinear Sci. Appl. , 5 (2012), 271-280
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P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl., 270 (2002), 1-15
##[15]
Y. Cui, L. Liu, X. Zhang, Uniqueness and existence of positive solutions for singular differential systems with coupled integral boundary value problems, Abstr. Appl. Anal., Art. ID 340487, 2013 (2013), 1-9
##[16]
A. Debbouche, J. J. Nieto, Sobolev type fractional abstract evolution equations with nonlocal conditions and optimal multi-controls, Appl. Math. Comput., 245 (2014), 74-85
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Y. Gambo et al., On Caputo modification of the Hadamard fractional derivatives, Adv. Difference Equ., 2014 (2014), 1-10
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C. S. Goodrich, Existence of a positive solution to systems of differential equations of fractioanl order, Comput. Math. Appl., 62 (2011), 1251-1268
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A. Guezane-Lakoud, R. Khaldi, Solvability of a two-point fractional boundary value problem, J. Nonlinear Sci. Appl., 5 (2012), 64-73
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M. Hao, C. Zhai , Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order, J. Nonlinear Sci. Appl., 7 (2) (2014), 131-137
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J. Henderson, R. Luca, Positive solutions for a system of nonlocal fractional boundary value problems, Fract. Calc. Appl. Anal., 16 (2013), 985-1008
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F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Adv. Difference Equ., 2012 (2012), 1-142
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J. Jiang, L. Liu, Y. Wu, Positive solutions to singular fractional differential system with coupled boundary conditions, Commun. Nonlinear Sci. Numer. Simulat., 18 (2013), 3061-3074
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Boston (2006)
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M. A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff Gronigen, Netherland (1964)
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A. Leung, A semilinear reaction-diffusion prey-predator system with nonlinear coupled boundary conditions: equilibrium and stability, Indiana Univ. Math., 31 (1982), 223-241
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Y. Li, H. Zhang, Positive solutions for a nonlinear higher order differential system with coupled integral boundary conditions, J. Appl. Math., Art. ID 901094, 2014 (2014), 1-7
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Y. Liu, H. Shi, Existence of unbounded positive solutions for BVPs of singular fractional differential equations, J. Nonlinear Sci. Appl., 5 (2012), 281-293
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S. Liu, G. Wang, L. Zhang, Existence results for a coupled system of nonlinear neutral fractional differential equations, Appl. Math. Lett., 26 (2013), 1120-1124
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J. A. Nanware, D. B. Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl., 7 (4) (2014), 246-254
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T. Qiu, Z. Bai, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Nonlinear Sci. Appl., 1 (3) (2008), 123-131
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C. V. Pao, Finite difference reaction-diffusion systems with coupled boundary conditions and time delays, J. Math. Anal. Appl., 272 (2002), 407-434
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M. Rehman, R. Khan, A note on boundary value problems for a coupled system of fractional differential equations, Comput. Math. Appl., 61 (2011), 2630-2637
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P. Thiramanus, S. K. Ntouyas, J. Tariboon, Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions, Abstr. Appl. Anal., Art. ID 902054, 2014 (2014), 1-9
##[35]
Y. Wang, L. Liu, Y. Wu, Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters, Adv. Differ. Equ, 2014 (2014), 1-268
##[36]
W. Yang, Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions, Comput. Math. Appl., 63 (2012), 288-297
##[37]
W. Yang, Positive solutions for nonlinear Caputo fractional differential equations with integral boundary conditions, J. Appl. Math. Comput., 44 (2014), 39-59
##[38]
W. Yang, Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions, Appl. Math. Comput., 244 (2014), 702-725
##[39]
W. Yang, Positive solutions for singular Hadamard fractional differential system with four-point coupled boundary conditions, J. Appl. Math. Comput., doi: 10.1007/s12190-014-0843-9. (2014)
##[40]
C. Yuan, Two positive solutions for (n - 1; 1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations, Commun. Nonlinear Sci. Numer. Simulat., 17 (2012), 930-942
##[41]
C. Yuan et al., Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions, Electron. J. Qual. Theory Differ. Equ., 13 (2012), 1-17
##[42]
Y. Zou, Y. Cui, Monotone iterative method for differential systems with coupled integral boundary value problems, Bound. Value Probl., 2013 (2013), 1-245
##[43]
Y. Zou, L. Liu, Y. Cui , The existence of solutions for four-point coupled boundary value problems of fractional differential equations at resonance, Abstr. Appl. Anal., Art. ID 314083, 2014 (2014), 1-8
]
Coupled fixed point theorems for compatible mappings in partially ordered \(G\)-metric spaces
Coupled fixed point theorems for compatible mappings in partially ordered \(G\)-metric spaces
en
en
In this paper, we prove coupled coincidence and coupled common fixed point theorems for compatible
mappings in partially ordered G-metric spaces. The results on fixed point theorems are generalizations of
some existing results. We also give an example to support our results.
130
141
Jianhua
Chen
Department of Mathematics
Nanchang University
P. R. China
cjh19881129@163.com
Xianjiu
Huang
Department of Mathematics
Nanchang University
P. R. China
xjhuangxwen@163.com
partially ordered set
couple coincidence point
coupled fixed point
compatible mappings
G-metric space.
Article.5.pdf
[
[1]
M. Abbas, M. A. Khan, S. Radenović, Common coupled fixed point theorem in cone metric space for \(w^*\)-compatible mappings , Appl. Math. Comput., 217 (2010), 195-202
##[2]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116
##[3]
H. Aydi, B. Damjanović, B. Samet, W. Shatanawi, Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces , Math. Comput. Modelling, 54 (2011), 2443-2450
##[4]
T. G. Bhaskar, V. Lakshmikantham , Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
##[5]
B. S. Choudhury, A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., 73 (2010), 2524-2531
##[6]
B. S. Choudhury, P. Maity, Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling, 54 (2011), 73-79
##[7]
R. Chugh, T. Kadian, A. Rani, B. E. Rhoades, Property P in G-metric spaces, Fixed Point Theory Appl., 2010 (2010), 1-12
##[8]
Lj. Ćirić, N. Cakić, M. Rajović, J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2008 (2008), 1-11
##[9]
Lj. Ćirić, D. Mihet, R. Saadati, Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology Appl., 156(17) (2009), 2838-2844
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M. Jain, K. Tas, B. E. Rhoades, N. Gupta, Coupled fixed point theorems for generalized symmetric contractions in partially ordered metric spaces and applications, J. Comput. Anal. Appl., 16 (2014), 438-454
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E. Karapinar, P. Kumam, I. Merhan, Coupled fixed point theorems on partially ordered G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-13
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V. Lakshmikantham, Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
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N. V. Luong, N. X. Thuan , Coupled fixed point theorems in partially ordered G-metric spaces, Math. Comput. Modelling, 55 (2012), 1601-1609
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S. A. Mohiuddine, A. Alotaibi, Coupled coincidence point theorems for compatible mappings in partially ordered intuitionistic generalized fuzzy metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-18
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Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297
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Z. Mustafa, H. Obiedat, F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008 (2008), 1-12
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Z. Mustafa, W. Hatanawi, M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., 2009 (2009), 1-10
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Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., 2009 (2009), 1-10
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H. K. Nashine, B. Samet , Fixed point results for mappings satisfying (\(\psi,\varphi\))-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 2201-2209
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H. K. Nashine, Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., 5 (2012), 1-13
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B. Samet , Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 72 (2010), 4508-4517
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W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl., 60 (2010), 2508-2515
##[23]
W. Shatanawi, Fixed point theory for contractive mappings satisfying \(\Phi\)-maps in G-metric spaces, Fixed Point Theory Appl., 2010 (2010), 1-9
]
Uniqueness and global exponential stability of almost periodic solution for Hematopoiesis model on time scales
Uniqueness and global exponential stability of almost periodic solution for Hematopoiesis model on time scales
en
en
This paper deals with almost periodic Hematopoiesis dynamic equation on time scales. By applying a
novel method based on the fixed point theorem of decreasing operator, we establish sufficient conditions
for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which
converges to the almost periodic positive solution. Moreover, we investigate global exponential stability of
the almost periodic positive solution by means of Gronwall inequality.
142
152
Zhijian
Yao
Department of Mathematics and Physics
Anhui Jianzhu University
China
zhijianyao@126.com
Hematopoiesis model on time scales
almost periodic solution
global exponential stability
fixed point theorem of decreasing operator
exponential dichotomy.
Article.6.pdf
[
[1]
M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston (2001)
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M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston (2003)
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D. Cheban, C. Mammana, Invariant manifolds, global attractors and almost periodic solutions of nonautonomous difference equations, Nonlinear Analysis: TMA, 56 (2004), 465-484
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J. Zhang, M. Fan, H. Zhu, Existence and roughness of exponential dichotomies of linear dynamic equations on time scales, Computers and Mathematics with Applications, 59 (2010), 2658-2675
]
Coupled fixed point theorems with respect to binary relations in metric spaces
Coupled fixed point theorems with respect to binary relations in metric spaces
en
en
In this paper we present a new extension of coupled fixed point theorems in metric spaces endowed with
a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in
this coupled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed
to hold on elements that are comparable in the binary relation. Next on the basis of the coupled fixed
point theorems, we prove the existence and uniqueness of positive definite solutions of a nonlinear matrix
equation.
153
162
Mohammad Sadegh
Asgari
Department of Mathematics, Faculty of Science
Islamic Azad University, Central Tehran Branch
Iran
moh.asgari@iauctb.ac.ir;msasgari@yahoo.com
Baharak
Mousavi
Department of Mathematics, Faculty of Science
Islamic Azad University, Central Tehran Branch
Iran
baharak82mousavi@gmail.com
Coupled fixed point
reflexive relation
matrix equations
positive define solution.
Article.7.pdf
[
[1]
M. Abbas, W. Sintunavarat, P. Kumam, Coupled fixed point of generalized contractive mappings on partially ordered G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-14
##[2]
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The elliptic sinh-Gordon equation in the half plane
The elliptic sinh-Gordon equation in the half plane
en
en
Boundary value problems for the elliptic sinh-Gordon equation formulated in the half plane are studied
by applying the so-called Fokas method. The method is a significant extension of the inverse scattering
transform, based on the analysis of the Lax pair formulation and the global relation that involves all known
and unknown boundary values. In this paper, we derive the formal representation of the solution in terms
of the solution of the matrix Riemann-Hilbert problem uniquely defined by the spectral functions. We also
present the global relation associated with the elliptic sinh-Gordon equation in the half plane. We in turn
show that given appropriate initial and boundary conditions, the unique solution exists provided that the
boundary values satisfy the global relation. Furthermore, we verify that the linear limit of the solution
coincides with that of the linearized equation known as the modified Helmhotz equation.
163
173
Guenbo
Hwang
Department of Mathematics
Daegu University
Korea
ghwang@daegu.ac.kr
Boundary value problems
elliptic PDEs
sinh-Gordon equation
integrable equation.
Article.8.pdf
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