]>
2014
7
2
ISSN 2008-1898
79
Existence of solutions to the state dependent sweeping process with delay
Existence of solutions to the state dependent sweeping process with delay
en
en
In this paper, we prove, via new projection algorithm, the existence of solutions for functional differential
inclusion governed by state dependent sweeping process with perturbation depending on all variables and
with delay.
70
77
Touma
Haddad
Département de Mathématique, Faculté des Sciences Exactes et Informatique
Université de Jijel
Algérie
touma.haddad@yahoo.com
Tahar
Haddad
Laboratoire LMPA, Département de Mathématiques, Faculté des Sciences Exactes et Informatique
Université de Jijel
Algérie
haddadtr2000@yahoo.fr
functional differential inclusion
normal cone
sweeping process
perturbation
delay.
Article.1.pdf
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Fixed point theorems for compatible and subsequentially continuous mappings in Menger spaces
Fixed point theorems for compatible and subsequentially continuous mappings in Menger spaces
en
en
In the present paper, we prove common fixed point theorems using the notions of compatibility and subsequentially continuity (alternately subcompatibility and reciprocally continuity) in Menger spaces. We also
give a common fixed point theorem satisfying an integral analogue. As applications to our results, we obtain
the corresponding fixed point theorems in metric spaces. Some illustrative examples are also given which
demonstrate the validity of our results.
78
89
Sunny
Chauhan
Near Nehru Training Centre
India
sun.gkv@gmail.com
B. D.
Pant
Government Degree College
India
badridatt.pant@gmail.com
Menger space
compatible mappings
reciprocally continuity
occasionally weakly compatible mappings
subcompatible mappings
subsequentially continuity.
Article.2.pdf
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J.-X. Fang, Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal., 70(1) (2009), 184-193
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D. Gopal, M. Imdad, Some new common fixed point theorems in fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 57(2) (2011), 303-316
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]
Unique common fixed point theorems on partial metric spaces
Unique common fixed point theorems on partial metric spaces
en
en
We prove the existence of the unique common fixed point theorems for self mappings which are weakly
compatible satisfying some contractive conditions on partial metric spaces. Furthermore, we also prove the
result on the continuity in the set of common fixed points for self mappings on partial metric spaces.
90
101
Anchalee
Kaewcharoen
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
anchaleeka@nu.ac.th
Tadchai
Yuying
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
tadchai99@hotmail.com
Common fixed points
Weakly compatible mappings
Coincidence points
Partial metric spaces.
Article.3.pdf
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M. Abbas, G. V. R. Babu, G. N. Alemayehu, On common fixed points of weakly compatible mappings satisfying generalized condition, Filomat, 25 (2011), 9-19
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M. Abbas, B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces , Appl. Math. Comput., 215 (2009), 262-269
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]
On a new class of abstract impulsive functional differential equations of fractional order
On a new class of abstract impulsive functional differential equations of fractional order
en
en
In this paper, we prove the existence and uniqueness of mild solutions for the impulsive fractional differential
equations for which the impulses are not instantaneous in a Banach space H. The results are obtained by
using the analytic semigroup theory and the fixed points theorems.
102
114
Pradeep
Kumar
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
India
prdipk@gmail.com
Dwijendra N.
Pandey
Department of Mathematics
Indian Institute of Technology Roorkee
India
dwij.iitk@gmail.com
D.
Bahuguna
Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
India
dhiren@iitk.ac.in
Impulsive fractional differential equations
Analytic semigroup
Fixed point theorems.
Article.4.pdf
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J. Wang, M. Fečkan, Y. Zhou, On the new concept of solutions and existence results for impulsive fractional evolution equations, Dyn. Partial Differ. Equ., 8 (2011), 345-361
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X. Li, F. Chen, Xuezhu Li , Generalized anti-periodic boundary value problems of impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 28-41
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V. Kavitha, M. Mallika Arjunan, C. Ravichandran, Existence results for impulsive systems with nonlocal conditions in Banach spaces , J. Nonlinear Sci. Appl., 4 (2011), 138-151
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T. Gunasekar, F. P. Samuel, M. Mallika Arjunan, Existence results for impulsive neutral functional integrodifferential equation with infinite delay, J. Nonlinear Sci. Appl., 6 (2013), 234-243
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A. Anguraj, M. Mallika Arjunan, E. M. Hernández, Existence results for an impulsive neutral functional differential equation with state-dependent delay, Appl.Anal., 86 (2007), 861-872
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C. Cuevas, G. N'Guérékata, M. Rabelo, Mild solutions for impulsive neutral functional differential equations with state- dependent delay, Semigroup Forum, 80 (2010), 375-390
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E. Hernández, A. Anguraj, M. Mallika Arjunan, Existence results for an impulsive second order differential equation with state-dependent delay, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 17 (2010), 287-301
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M. Maliika Arjunan, V. Kavitha, Existence results for impulsive neutral functional differential equation with state-dependent delay, Electorn. J. Qual. Theory Differ. Equ., (2009), 1-13
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Y. K. Chang, A. Anguraj, M. Mallika Arjunan, Existence results for impulsive neutral functional differential equations with infinite delay, Nonlinear Anal. Hybrid Syst., 2 (2008), 209-218
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Y. K. Chang, J. Juan Nieto, Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Funct. Anal. Optim., 30 (2009), 227-244
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W. Ding, Yu. Wang, New result for a class of impulsive differential equation with integral boundary conditions, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 1095-1105
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Ch. Bai, Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J. Appl. Math. Comput., 39 (2012), 421-443
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M. Gisle Mophou , Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Anal., 72 (2010), 1604-1615
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Y. Liu, Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 2604-2625
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G. Wang, B. Ahmad, L. Zhang, On impulsive boundary value problems of fractional differential equations with irregular boundary conditions, Abstr. Appl. Anal., (2012), 1-15
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A. Debbouche, D. Baleanu, Controllability of fractional evolution nonlocal impulsive quasilinear delay integro- differential systems, Comput. Math. Appl., 62 (2011), 1442-1450
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N. Marcos Rabelo, M. Henrique, G. Siracusa , Existence of integro-differential solutions for a class of abstract partial impulsive differential equations, J. Inequal. Appl., (2011), 1-19
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D. Zhang, Multiple solutions of nonlinear impulsive differential equations with Dirichlet boundary conditions via variational method, Results Math., 63 (2013), 611-628
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J. Wang, Y. Zhou, Existence and controllability results for fractional semilinear differential inclusions, Nonlinear Anal. Real World Appl., 12 (2011), 3642-3653
##[38]
M. Benchohra, J. Henderson, S. K. Ntouyas, Existence results for impulsive semilinear neutral functional differential equations in Banach spaces, Differential Equations Math. Phys., 25 (2002), 105-120
]
Existence of solutions for quasi-linear impulsive functional integrodifferential equations in Banach spaces
Existence of solutions for quasi-linear impulsive functional integrodifferential equations in Banach spaces
en
en
We study the existence of mild solutions for quasilinear impulsive integrodifferential equation in Banach
spaces. The results are established by using Hausdorff's measure of noncompactness and fixed point theorem.
Application is provided to illustrate the theory.
115
125
Francis Paul
Samuel
Department of Mathematics and Physics
University of Eastern Africa
Kenya
paulsamuel_f@yahoo.com
Krishnan
Balachandran
Department of Mathematics
Bharathiar University
India
kbkb1956@yahoo.com
Mild solution
nonlocal conditions
impulsive condition
Hausdorff's measure of noncompactness
fixed point theorem.
Article.5.pdf
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M. Mallika Arjunan, V. Kavitha, S. Selvi , Existence results for impulsive differential equations with nonlocal conditions via measures of noncompactness, J. Nonlinear Sci. Appl., 5 (2012), 195-205
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A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York (1983)
]
Best Proximity Point Iteration for Nonexpensive Mapping in Banach Spaces
Best Proximity Point Iteration for Nonexpensive Mapping in Banach Spaces
en
en
In this paper we prove existence theorems of best proximity points in Banach spaces. Also an iterative
approximation of the best proximity point of a nonexpensive mapping in Banach space is developed.
126
130
Mohammad Reza
Haddadi
Faculty of Mathematics
Ayatollah Boroujerdi University
Iran
haddadi@abru.ac.ir
Best proximity pair
best proximity point
cyclic contractive map
P-property.
Article.6.pdf
[
[1]
S. Chauhan, B. D. Pant, Fixed point theorems for compatible and subsequentially continuous mappings in Menger spaces, J. Nonlinear Sci. Appl., 7 (2001), 78-89
##[2]
A. Abkar, M. Gabeleh, Best proximity points of non-self mappings, TOP, 21 (2013), 287-295
##[3]
A. A. Eldred, W. A. Kirk, P. Veeramani, Proximinal normal structure and relatively nonexpansive mappings, Studia Math, 171 (2005), 283-293
##[4]
A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points , J. Math. Anal. Appl., 323 (2006), 1001-1006
##[5]
M. Gabeleh, Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces , J. Optim. Theory Appl. , 158 (2013), 615-625
##[6]
M. R. Haddadi, S. M. Moshtaghioun, Some Results on the Best Proximity Pair, Abstract and Applied Analysis, ID 158430, 2011 (2011), 1-9
##[7]
H. Kumar Nashine, P. Kumam, C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory and Applications, 2013:95 (2013)
##[8]
Yunus Purtasa, Hukmi Kiziltunc, Weak and strong convergence of an explicit iteration process for an asymptotically quasi-i-nonexpansive mapping in Banach spaces , J. Nonlinear Sci. Appl., 5 (2012), 403-411
##[9]
S. Sadiq Basha, Best proximity points: global optimal approximate solution, J Global Optim. , doi:10.1007/s10898- 009-9521-0 (2010)
##[10]
S. Sadiq Basha, Extensions of Banachs contraction principle, Numer Funct Anal Optim, 31 (2010), 569-576
##[11]
Raj V. Sankar, P. Veeramani , Best proximity pair theorems for relatively nonexpansive mappings, Appl Gen Topol, 10(1) (2009), 21-28
##[12]
Raj V. Sankar, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Analysis, 74 (2011), 4804-4808
##[13]
H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl., 116 (2003), 659-678
]
Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order
Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order
en
en
In this paper, by using Schauder fixed point theorem, we study the existence of at least one positive solution
to a coupled system of fractional boundary value problems given by
\[
\begin{cases}
-D^{\nu_1}_{0^+}y_1(t) = \lambda_1a_1(t)f(t, y_1(t), y_2(t)) + e_1(t),\\
-D^{\nu_2}_{0^+}y_2(t) = \lambda_2a_2(t)g(t, y_1(t), y_2(t)) + e_2(t),
\end{cases}
\]
where \(\nu_1,\nu_2\in (n - 1; n]\) for \(n > 3\) and \(n \in N\), subject to the boundary conditions \(y^(i)_1 (0) = 0 = y^(i)_2 (0)\), for
\(0 \leq i \leq n - 2\), and \([D^{\alpha}_{0^+}y_1(t)]_{t=1}=0=[D^{\alpha}_{0^+}y_2(t)]_{t=1}\), for \(1 \leq\alpha\leq n - 2\).
131
137
Mengru
Hao
School of Mathematical Sciences
Shanxi University
P.R. China
mengru314314@126.com
Chengbo
Zhai
School of Mathematical Sciences
Shanxi University
P.R. China
cbzhai@sxu.edu.cn
Fractional differential equation
Schauder fixed point theorem
Positive solution.
Article.7.pdf
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]
Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces
Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces
en
en
The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration
process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real
uniformly convex Banach spaces if E satisfies Opial's condition or the dual \(E^*\) of \(E\) has the Kedec-Klee
property. Our results extend and improve some known corresponding results from the existing literature.
138
149
G. S.
Saluja
Department of Mathematics and I.T.
Govt. N.P.G. College of Science
India
saluja_1963@rediffmail.com;saluja1963@gmail.com
Asymptotically quasi-nonexpansive non-self mappings
common fixed point
the modified two-step iteration process with errors for non-self maps
uniformly convex Banach space
weak convergence.
Article.8.pdf
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]