]>
2012
5
3
ISSN 2008-1898
90
Some further applications of KKM theorem in topological semilattices
Some further applications of KKM theorem in topological semilattices
en
en
In this paper, we obtain some further applications of KKM theorem in setting of topological semilattices such
as Ky Fan-Kakutani type fixed point theorem, Sion-Neumann type set-valued minimax theorem, set-valued
vector optimization problems.
161
173
Nguyen The
Vinh
Department of Mathematical Analysis
University of Transport and Communications
Vietnam
thevinhbn@gmail.com
generalized Ky Fan minimax inequality
set-valued mapping
topological semilattices
\(C_\Delta\)-quasiconvex
upper (lower) \(C\)-continuous
fixed point
Nash equilibrium.
Article.1.pdf
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N. T. Vinh, Systems of generalized quasi-Ky Fan inequalities and Nash equilibrium points with set-valued maps in topological semilattices , PanAmer. Math. J. , 19 (2009), 79-92
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G. X. Z. Yuan, KKM Theory and Applications in Nonlinear Analysis, Marcel Dekker Inc., New York (1999)
]
Existence of mild solutions of random impulsive functional differential equations with almost sectorial operators
Existence of mild solutions of random impulsive functional differential equations with almost sectorial operators
en
en
By using the theory of semigroups of growth \(\alpha\), we prove the existence and uniqueness of the mild solution
for the random impulsive functional differential equations involving almost sectorial operators. An example
is given to illustrate the theory.
174
185
A.
Anguraj
Department of Mathematics
P. S.G. College of Arts and Science
India
angurajpsg@yahoo.com
M. C.
Ranjini
Department of Mathematics
P. S. G. College of Arts and Science
India
ranjiniprasad@gmail.com
Impusive differential equations
random impulses
almost sectorial operator
semigroup of growth \(\alpha\)
mild solution
Article.2.pdf
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Eduardo .M. Hernandez, Marco Rabello ,H. R. Henriquez, Existence of solutions for impulsive partial neutral functional differential equations, J.Math.Anal.Appl. , 331 (2007), 1135-1158
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V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989)
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Rogovchenko, V. Yu, Impusive evolution systems: main results and new trends, Dynamics Contin. Diser. Impulsive Sys., 3 (1997), 57-88
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A. Anguraj, A. Vinodkumar, Existence and Uniqueness of Neutral Functional Differential Equations with random impulses, International Journal of Nonlinear Science, 8 (2009), 412-418
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S. J. Wu, Y. R. Duan, Oscillation, stability and boundedness of second-order differential systems with random impulses, Computers and Mathematics with Applications, 49(9-10) (2005), 1375-1386
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A. Anguraj, Shujin Wu, A. Vinodkumar , The Existence and Exponential stability of semilinear functional differential equations with random impulses under non-uniqueness, Nonlinear Analysis:Theory, Methods and Applications, 74 (2011), 331-342
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E. M. Hernandez, On a class of abstract functional differential equations involving almost sectorial operators, , 3, 1 (2011), 1-10
]
Coupled fixed point theorems in d-complete topological spaces
Coupled fixed point theorems in d-complete topological spaces
en
en
In this paper, we obtain prove two common coupled fixed point theorems in Hausdorff d- complete topological
spaces.
186
194
K. P. R.
Rao
Department of Applied Mathematics
Acharya Nagarjuna University---Dr. M.R. Appa Row Campus
India
kprrao2004@yahoo.com
S. Hima
Bindu
Department of Mathematics
CH. S. D. St. Theresa's Junior College for women
India
s.hima_bindu@yahoo.com
Md. Mustaq
Ali
Department of Applied Mathematics
Acharya Nagarjuna University--Dr. M.R. Appa Row Campus
India
alimustaq9@gmail.com
Coupled fixed points
d-complete space
weakly compatible maps.
Article.3.pdf
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M. Abbas, M. Alikhan, S. Radenovic, Common coupled fixed point theorems in cone metric spaces for W-compatible mappings, Applied Mathematics and Computation, doi: 10.1016/ j.amc2010.05.042. , 217 (1) (2010), 195-202
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B. S. Choudhury, A. Kundu , A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Analysis, doi: 10.1016/ j.na.2010.06.025. , 73 (8) (2010), 2524-2531
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Hui-Sheng Ding, Lu Li , Coupled fixed point theorems in partial ordered cone metric spaces, Filomat , 25 (2) (2011), 137-149
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]
Existence results for impulsive differential equations with nonlocal conditions via measures of noncompactness
Existence results for impulsive differential equations with nonlocal conditions via measures of noncompactness
en
en
In this paper, we study the existence of integral solutions for impulsive evolution equations with nonlocal
conditions where the linear part is nondensely defined. Some existence results of integral solutions to
such problems are obtained under the conditions in respect of the Hausdorff's measure of noncompactness.
Example is provided to illustrate the main result.
195
205
M. Mallika
Arjunan
Department of Mathematics
Karunya University
India
arjunphd07@yahoo.co.in
V.
Kavitha
Department of Mathematics
Karunya University
India
kavi_velubagyam@yahoo.co.in
S.
Selvi
Department of Mathematics
Muthayammal College of Arts & Science
India
sselvimaths@yahoo.com
Impulsive differential equations
nondensely defined
noncompact measures
nonlocal conditions
integral solutions
semigroup theory.
Article.4.pdf
[
[1]
A. Anguraj, M. Mallika Arjunan, Existence and uniqueness of mild and classical solutions of impulsive evolution equations, Electronic Journal of Differential Equations, 111 (2005), 1-8
##[2]
A. Anguraj, M. Mallika Arjunan, Existence results for an impulsive neutral integro-differential equations in Banach spaces, Nonlinear Studies, 16(1) (2009), 33-48
##[3]
H. Akca, A. Boucherif, V. Covachev, Impulsive functional differential equations with nonlocal conditions, Inter. J. Math. Math. Sci., 29:5 (2002), 251-256
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D. D. Bainov, P. S. Simeonov , Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical Group, England (1993)
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J. Banas, K. Goebel , Measure of Noncompactness in Banach Spaces, in: Lecture Notes in Pure and Appl. Math., 60, Marcel Dekker, New York (1980)
##[6]
M. Benchohra, S. K. Ntouyas, Existence of mild solutions for certain delay semilinear evolution inclusions with nonlocal condition, Dynam. Systems Appl., 9:3 (2000), 405-412
##[7]
M. Benchohra, S. K. Ntouyas, Existence of mild solutions of semilinear evolution inclusions with nonlocal conditions, Georgian Math. J., 7 (2000), 221-230
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M. Benchohra, S. K. Ntouyas, Existence and controllability results for nonlinear differential inclusions with nonlocal conditions, J. Appl. Anal., 8 (2002), 31-46
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T. Cardinali, P. Rubbioni, Impulsive semilinear differential inclusion: Topological structure of the solution set and solutions on non-compact domains, Nonlinear Anal., 14 (2008), 73-84
##[13]
Y. K. Chang, A. Anguraj, M. Mallika Arjunan, Existence results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions, J. Appl. Math. Comput., 28 (2008), 79-91
##[14]
Y. K. Chang, A. Anguraj, M. Mallika Arjunan, Existence results for impulsive neutral functional differential equations with infinite delay, Nonlinear Anal.: Hybrid Systems, 2(1) (2008), 209-218
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Y. K. Chang, V. Kavitha, M. Mallika Arjunan, Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators, Nonlinear Anal.: Hybrid Systems, 4(1) (2010), 32-43
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Z. Fan, Q. Dong, G. Li, Semilinear didderential equations with nonlocal conditions in Banach spaces, International Journal of Nonlinear Science, 2(3) (2006), 131-139
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Z. Fan, Existence of nondensely defined evolution equations with nonlocal conditions, Nonlinear Anal., 70 (2009), 3829-3836
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Z. Fan, Impulsive problems for semilinear differential equations with nonlocal conditions, Nonlinear Anal., 72(2) (2010), 1104-1109
##[20]
M. Kamenskii, V. Obukhovskii, P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, De Gruyter Ser: Nonlinear Anal. Appl., 7, de Gruyter, Berlin (2001)
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H. Kellerman, M. Heiber, Integrated semigroups, J. Funct. Anal., 84 (1989), 160-180
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V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989)
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J. Liang, J. H. Liu, Ti-Jun Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Model., 49 (2009), 798-804
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J. H. Liu , Nonlinear impulsive evolution equations, Dynam. Contin. Discrete Impuls. Sys., 6 (1999), 77-85
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H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal., 4 (1980), 985-999
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A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995)
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B. Selvaraj, M. Mallika Arjunan, V. Kavitha, Existence of solutions for impulsive nonlinear differential equations with nonlocal conditions, J. Korean Society for Industrial and Applied Mathematics, 13(3) (2009), 203-215
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K. Yosida, Functional Analysis, 6th edn., Springer, Berlin (1980)
]
Controllability results for impulsive differential systems with finite delay
Controllability results for impulsive differential systems with finite delay
en
en
This paper establishes some sufficient conditions for controllability of impulsive functional differential equations with finite delay in a Banach space. The results are obtained by using the measures of noncompactness
and Monch fixed point theorem. Particularly, we do not assume the compactness of the evolution system.
Finally, an example is provided to illustrate the theory.
206
219
S.
Selvi
Department of Mathematics
Muthayammal College of Arts & Science
India
sselvimaths@yahoo.com
M. Mallika
Arjunan
Department of Mathematics
Karunya University
India
arjunphd07@yahoo.co.in
Controllability
Impulsive differential equations
Measures of noncompactness
Semigroup theory
Fixed point.
Article.5.pdf
[
[1]
A. Anguraj, M. Mallika Arjunan, Existence and uniqueness of mild and classical solutions of impulsive evolution equations, Electron J. Differential Equations, 111 (2005), 1-8
##[2]
A. Anguraj, M. Mallika Arjunan, Existence results for an impulsive neutral integro-differential equations in Banach spaces, Nonlinear Stud., 16(1) (2009), 33-48
##[3]
D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical Group, England (1993)
##[4]
J. Banas, K. Goebel , Measure of Noncompactness in Banach Spaces, in: Lecture Notes in Pure and Applied Matyenath, Marcel Dekker, New York (1980)
##[5]
M. Benchohra, J. Henderson, S. K. Ntouyas , Existence results for impulsive multivalued semilinear neutral functional inclusions in Banach spaces , J. Math. Anal. Appl., 263 (2001), 763-780
##[6]
L. Chen, G. Li , Approximate controllability of impulsive differential equations with nonlocal conditions, Int. J. Nonlinear Sci., 10 (2010), 438-446
##[7]
Z. Fan, Impulsive problems for semilinear differential equations with nonlocal conditions, Nonlinear Anal., 72 (2010), 1104-1109
##[8]
Z. Fan, G. Li , Existence results for semilinear differential equations with nonlocal and impulsive conditions, J. Funct. Anal., 258 (2010), 1709-1727
##[9]
E. Hernandez, M. Pierri, G. Goncalves, Existence results for an impulsive abstract partial differential equation with state-dependent delay, Comput. Math. Appl., 52 (2006), 411-420
##[10]
E. Hernandez, M. Rabello, H. Henriaquez, Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Appl., 331 (2007), 1135-1158
##[11]
S. Ji, G. Li, M. Wang, Controllability of impulsive differential systems with nonlocal conditions, Appl.Math. Comput., 217 (2011), 6981-6989
##[12]
S. Ji, S. Wen, Nonlocal cauchy problem for Impulsive differential equations in Banach spaces, Int. J. Nonlinear Sci., 10 (2010), 88-95
##[13]
M. Kamenskii, V. Obukhovskii, P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, De Gruyter, (2001)
##[14]
V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989)
##[15]
M. Li, M. Wang, F. Zhang, Controllability of impulsive functional differential systems in Banach spaces, Chaos, Solitons and Fractals, 29 (2006), 175-181
##[16]
H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal., 4 (1980), 985-999
##[17]
V. Obukhovski, P. Zecca, Controllability for systems governed by semilinear differential inclusions in a Banach space with a noncompact semigroup, Nonlinear Anal., 70 (2009), 3424-3436
##[18]
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Newyork (1983)
##[19]
B. Radhakrishnan, K. Balachandran, Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay, Nonlinear Anal., 5 (2011), 655-670
##[20]
A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995)
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C. Travis, G. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc., 200 (1974), 395-418
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R. Ye, Existence of solutions for impulsive partial neutral functional differential equation with infinite delay , Nonlinear Anal., 73 (2010), 155-162
]
On some common fixed point theorems with PPF dependence in Banach spaces
On some common fixed point theorems with PPF dependence in Banach spaces
en
en
In this paper, some results concerning the existence of common fixed points, coincidence points and approximating fixed points with PPF dependence for the pairs of operators in Banach spaces satisfying a generalized
contractive condition are proved. The novelty of the present work lies in the fact that the domain and the
range spaces of the operators in questions are not same and all the results are obtained via constructive
methods. Our results generalize and extend the fixed point theorems with PPF dependence of Bernfeld et
al. [S. R. Bernfeld, V. Lakshmikatham and Y. M. Reddy, Applicable Anal. 6 (1977), 271-280] and Dhage
[B. C. Dhage, Fixed point Theory, (to appear)] under more general contractive conditions.
220
232
Bapurao C.
Dhage
Kasubai,
Gurukul Colony,
India
bcdhage@yahoo.co.in; bcdhage@gmail.com
Banach space
Fixed point theorem
PPF dependence.
Article.6.pdf
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[1]
S. R. Bernfeld, V. Lakshmikatham, Y. M. Reddy , Fixed point theorems of operators with PPF dependence in Banach spaces, Applicable Anal. , 6 (1977), 271-280
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Lj. B. Ćirić, A generalization of Banach's contraction principle, PAMS, 45 (1974), 267-273
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B. C. Dhage , Fixed point theorems with PPF dependence and functional differential equations, Fixed point Theory, 12 (2011), -
##[5]
B. C. Dhage, Some basic random fixed point theorems with PPF dependence and functional random differential equations, Diff. Equ. Appl., 4 (2012), 181-195
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R. Kannan, Some results on fixed points II, Amer. Math. Monthly , 76 (1969), 405-408
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##[8]
B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. AMS , 226 (1977), 257-290
]
Convergence theorems of a general approximation method for common fixed points of a finite family of asymptotically-quasi nonexpansive mappings in Banach spaces
Convergence theorems of a general approximation method for common fixed points of a finite family of asymptotically-quasi nonexpansive mappings in Banach spaces
en
en
In this paper, we consider a general iterative scheme to approximate a common fixed point for a finite family
of asymptotically quasi-nonexpansive mappings. Several strong and weak convergence results are presented
in Banach spaces and an finite family of asymptotically quasi-nonexpansive mappings is constructed. Our
results generalize and extend many known results in the current literature.
232
242
Qiao-Li
Dong
College of Science
Civil Aviation University of China
China
dongqiaoli@ymail.com
Songnian
He
College of Science
Civil Aviation University of China
China
hesongnian2003@yahoo.com.cn
Bin-Chao
Deng
Technical economy and management specialty, School of Management
Tianjin University
China
dbchao1985@yahoo.com.cn
Modified Mann and Ishikawa iterations
Asymptotically quasi-nonexpansive mappings
Common fixed points
Weak and strong convergence
Uniformly convex Banach spaces.
Article.7.pdf
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K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically non-expansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174
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S. H. Khan, W. Takahasi , Approximating common fixed points of two asymptotically nonexpanisve mappings, Sci. Math. Jpn., 53 (2001), 143-148
##[4]
L. C. Ceng, P. Cubiotti, J. C. Yao, Appoximation of common fixed points of families of nonexpansive mappings, Taiwanese J. Math., 12 (2008), 487-500
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Y. Yao, J. C. Yao, H. Zhou, Appoximation methods for common fixed points of infinite countable family of nonexpansive mappings, Comput. Math. Appl. , 53 (2007), 1380-1389
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A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem
A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem
en
en
Viscosity iterations which include contraction mapping have been widely used to find solutions of equilibrium
problems. Here we introduce a modification of the viscosity iteration scheme by replacing the contraction
with a weak contraction. Weakly contractive mappings are intermediate to contractive and nonexpansive
mappings and are known to have unique fixed points in complete metric spaces. We apply this iteration to
the case of a generalized equilibrium problem. The special case where the weak contraction is a contraction
has also been discussed.
243
251
B. S.
Choudhury
Faculty of Bengal Engineering and Science University
India
binayak12@yahoo.co.in
Subhajit
Kundu
Department of Mathematics
Bengal Engineering and Science University
India
subhajit.math@gmail.com
Generalized Equilibrium problem
Viscosity approximation methods
Nonexpansive mappings
Weak contraction
Article.8.pdf
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