scholarly journals Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

scholarly journals Borsuk’s antipodal fixed points theorems for compact or condensing set-valued maps

2018 ◽  
Vol 7 (3) ◽  
pp. 307-311 ◽  
Author(s):  
Najla Altwaijry ◽  
Souhail Chebbi ◽  
Hakim Hammami ◽  
Pascal Gourdel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Large Class ◽  
Point Theorem ◽  
Vector Spaces ◽  
Compact Set ◽  
Topological Vector Spaces ◽  
Locally Convex

AbstractWe give a generalized version of the well-known Borsuk’s antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set-valued maps defined on closed subsets of locally convex topological vector spaces. These results contain corresponding results obtained in the literature for compact set-valued maps with convex values.

scholarly journals On the existence of solutions for vector quasiequilibrium problems

2019 ◽  
Vol 15 (3) ◽  
pp. 48
Author(s):  
Nguyen Xuan Hai ◽  
Nguyen Van Hung
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasiequilibrium Problems ◽  
Solution Sets ◽  
Topological Vector Spaces ◽  
Vector Quasiequilibrium Problems ◽  
Locally Convex

In this paper, we establish some existence theorems for vector quasiequilibrium problems in real locally convex Hausdorff topological vector spaces by using Kakutani-Fan-Glicksberg fixed-point theorem. Moreover, we also discuss the closedness of the solution sets for these problems. The results presented in the paper are new and improve some main results in the literature.

scholarly journals Existence of solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces

2003 ◽  
Vol 16 (2) ◽  
pp. 163-170 ◽  
Author(s):  
M. Kanakaraj ◽  
K. Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Topological Spaces ◽  
Sobolev Type ◽  
Multivalued Maps ◽  
Locally Convex

The existence of mild solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.

scholarly journals An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions

This paper studies the existence of solutions for a boundary value problem of nonlinear fractional hybrid differential inclusions by using a fixed point theorem due to Dhage (2006). The main result is illustrated with the aid of an example.

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

scholarly journals A System of Generalized Variational-Hemivariational Inequalities with Set-Valued Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhi-bin Liu ◽  
Jian-hong Gou ◽  
Yi-bin Xiao ◽  
Xue-song Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Directional Derivatives ◽  
Hemivariational Inequalities ◽  
Kkm Theorem ◽  
Special Cases ◽  
Generalized Directional Derivatives ◽  
Set Valued Mappings

By using surjectivity theorem of pseudomonotone and coercive operators rather than the KKM theorem and fixed point theorem used in recent literatures, we obtain some conditions under which a system of generalized variational-hemivariational inequalities concerning set-valued mappings, which includes as special cases many problems of hemivariational inequalities studied in recent literatures, is solvable. As an application, we prove an existence theorem of solutions for a system of generalized variational-hemivariational inequalities involving integrals of Clarke's generalized directional derivatives.

Fixed point theorem in subsets of topological vector spaces

2005 ◽  
Vol 340 (11) ◽  
pp. 815-818
Author(s):  
Youcef Askoura ◽  
Christiane Godet-Thobie
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Vector Spaces ◽  
Topological Vector Spaces

scholarly journals Fixed points, intersection theorems, variational inequalities, and equilibrium theorems

2000 ◽  
Vol 24 (2) ◽  
pp. 73-93 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Convex Sets ◽  
Quasi Equilibrium ◽  
Topological Vector Spaces ◽  
Abstract Economies ◽  
General Economic Equilibrium ◽  
Locally Convex

From a fixed point theorem for compact acyclic maps defined on admissible convex sets in the sense of Klee, we first deduce collectively fixed point theorems, intersection theorems for sets with convex sections, and quasi-equilibrium theorems. These quasi-equilibrium theorems are applied to give simple and unified proofs of the known variational inequalities of the Hartman-Stampacchia-Browder type. Moreover, from our new fixed point theorem, we deduce new variational inequalities which can be used to obtain fixed point results for convex-valued maps. Finally, various general economic equilibrium theorems are deduced in the forms of the Nash type, the Tarafdar type, and the Yannelis-Prabhakar type. Our results are stated for not-necessarily locally convex topological vector spaces and for abstract economies with arbitrary number of commodities and agents. Our new results extend a lot of known works with much simpler proofs.

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