A New Maximal Theorem in Product GFC-Spaces with Application to Systems of Generalized Mixed Vector Quasiequilibrium Problems

2013 ◽  
Vol 405-408 ◽  
pp. 3151-3154
Author(s):  
Kai Ting Wen
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Quasiequilibrium Problems ◽  
Maximal Element Theorem ◽  
Maximal Theorem ◽  
Vector Quasiequilibrium Problems ◽  
Element Theorem

In this paper, a new maximal element theorem is established in product GFC-spaces. As application, a new existence theorem of solutions for systems of generalized mixed vector quasi-equilibrium problems is obtained.

The Equilibrium Existence Theorem for Systems of General Quasiequilibrium Problems in GFC-Spaces

2014 ◽  
Vol 556-562 ◽  
pp. 4128-4132
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Kkm Mapping ◽  
Kkm Theorem ◽  
Equilibrium Existence ◽  
Quasiequilibrium Problems ◽  
Maximal Element Theorem ◽  
Matching Theorem ◽  
Element Theorem

In this paper, the GFC-KKM mapping is introduced and a GFC-KKM theorem is established in GFC-spaces. As applications, a matching theorem and a maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, an equilibrium existence theorem for systems of general quasiequilibrium problems is yielded in GFC-spaces.

scholarly journals System of Operator Quasi Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Suhel Ahmad Khan
Keyword(s):  
Maximal Element ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasi Equilibrium ◽  
Basic Tool ◽  
Maximal Element Theorem ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Element Theorem

We consider a system of operator quasi equilibrium problems and system of generalized quasi operator equilibrium problems in topological vector spaces. Using a maximal element theorem for a family of set-valued mappings as basic tool, we derive some existence theorems for solutions to these problems with and without involving Φ-condensing mappings.

scholarly journals On System of Generalized Vector Quasiequilibrium Problems with Applications

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
Jian-Wen Peng ◽  
Lun Wan
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Quasi Equilibrium ◽  
Vector Equilibrium Problems ◽  
Quasiequilibrium Problems ◽  
Special Cases ◽  
Vector Equilibrium ◽  
Vector Quasiequilibrium Problems ◽  
Vector Valued Functions ◽  
Vector Valued

We introduce a new system of generalized vector quasiequilibrium problems which includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and vector equilibrium problems, and so forth in literature as special cases. We prove the existence of solutions for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of generalized quasi-equilibrium problems and the generalized Debreu-type equilibrium problem for both vector-valued functions and scalar-valued functions.

scholarly journals The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qi-Qing Song
Keyword(s):  
Equilibrium Problem ◽  
Existence Result ◽  
Quasi Equilibrium ◽  
Topological Order ◽  
Stability Of Solutions ◽  
Maximal Elements ◽  
Quasiequilibrium Problems ◽  
Existence And Stability ◽  
Essential Set ◽  
Vector Quasiequilibrium Problems

In a topological sup-semilattice, we established a new existence result for vector quasiequilibrium problems. By the analysis of essential stabilities of maximal elements in a topological sup-semilattice, we prove that for solutions of each vector quasi-equilibrium problem, there exists a connected minimal essential set which can resist the perturbation of the vector quasi-equilibrium problem.

scholarly journals A Maximal Element Theorem inFWC-Spaces and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-18
Author(s):  
Haishu Lu ◽  
Qingwen Hu ◽  
Yulin Miao
Keyword(s):  
Equilibrium Problem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Minimax Problem ◽  
Lower And Upper Bounds ◽  
Weakly Convex ◽  
Maximal Element Theorem ◽  
Variational Relation Problem ◽  
Generalized Equilibrium ◽  
Element Theorem

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem inFWC-spaces. The results represented in this paper unify and extend some known results in the literature.

scholarly journals Approximate fixed points on almost convex sets

2004 ◽  
Vol 35 (3) ◽  
pp. 255-260
Author(s):  
J. E. C. Lope ◽  
R. M. Rey ◽  
M. Roque ◽  
P. W. Sy
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Maximal Element ◽  
Convex Sets ◽  
Maximal Element Theorem ◽  
Approximate Fixed Point ◽  
Almost Convex ◽  
Element Theorem

In this paper, we deduce a maximal element theorem on multimaps and an approximate fixed point theorem on almost convex sets. This generalizes the well-known Himmelberg fixed point theorem and also unifies recent results of Park and Tan [14] %cite{tan2} and Sy and Park [16].

scholarly journals Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mohammed Alshahrani ◽  
Qamrul Hasan Ansari ◽  
Suliman Al-Homidan
Keyword(s):  
Maximal Element ◽  
Optimization Problem ◽  
Existence Results ◽  
Kkm Theorem ◽  
Maximal Element Theorem ◽  
Element Theorem

We introduce nonsmooth vector quasi-variational-like inequalities (NVQVLI) by means of a bifunction. We establish some existence results for solutions of these inequalities by using Fan-KKM theorem and a maximal element theorem. By using the technique and methodology adopted in Al-Homidan et al. (2012), one can easily derive the relations among these inequalities and a vector quasi-optimization problem. Hence, the existence results for a solution of a vector quasi-optimization problem can be derived by using our results. The results of this paper extend several known results in the literature.

scholarly journals Existence of solutions for a system of quasi-variational relation problems and some applications

2015 ◽  
Vol 31 (1) ◽  
pp. 135-142
Author(s):  
ZHE YANG ◽  
Keyword(s):  
Nash Equilibrium ◽  
Maximal Element ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Quasi Equilibrium ◽  
Variational Inclusions ◽  
New Class

In this paper, we study the existence of solutions for a new class of systems of quasi-variational relation problems on different domains. As applications, we obtain existence theorems of solutions for systems of quasi-variational inclusions, systems of quasi-equilibrium problems, systems of generalized maximal element problems, systems of generalized KKM problems and systems of generalized quasi-Nash equilibrium problems on different domains. The results of this paper improve and generalize several known results on variational relation problems.

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