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.

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 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 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 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].

An RS-KKM Theorem in FC-Metric Spaces with the Application to Fixed Points

2013 ◽  
Vol 838-841 ◽  
pp. 2215-2218
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Maximal Element ◽  
Metric Spaces ◽  
Recent Literature ◽  
Kkm Theorem ◽  
Kkm Mappings ◽  
Section Theorem ◽  
Element Theorem ◽  
Ky Fan

In this paper, RS-KKM mappings are introduced and an RS-KKM theorem is established in noncompact complete FC-metric spaces. As applications, a Ky Fan section theorem, a maximal element theorem and a Fan-Browder type fixed point theorem are obtained in noncompact complete FC-metric spaces. These results unify, improve and generalize some known results in recent literature.

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.

A new maximal element theorem in -space with applications

2008 ◽  
Vol 68 (8) ◽  
pp. 2194-2203 ◽  
Author(s):  
Weiping Guo ◽  
Y.J. Cho
Keyword(s):  
Maximal Element ◽  
Maximal Element Theorem ◽  
Element Theorem

scholarly journals On D-KKM theorem and its applications

2003 ◽  
Vol 67 (1) ◽  
pp. 67-77 ◽  
Author(s):  
H. K. Pathak ◽  
M. S. Khan
Keyword(s):  
Variational Inequalities ◽  
Existence Results ◽  
Kkm Theorem ◽  
Maximal Elements ◽  
New Class ◽  
Kkm Mappings ◽  
Set Valued Mappings ◽  
Convex Setting

In this paper, we introduce a new class of set-valued mappings in a non-convex setting called D-KKM mappings and prove a general D-KKM theorem. This extends and improves the KKM theorem for several families of set-valued mappings, such as (X, Y), C(X, Y), C (X, Y), C (X, Y) and C (X, Y). In the sequel, we apply our theorem to get some existence results for maximal elements, generalised variational inequalities, and price equilibria.

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