scholarly journals The Hierarchical Minimax Inequalities for Set-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yen-Cherng Lin ◽  
Chin-Tzong Pang
Keyword(s):  
Equilibrium Problems ◽  
Vector Spaces ◽  
Minimax Inequalities ◽  
Topological Vector Spaces ◽  
Set Valued Mappings

We study the minimax inequalities for set-valued mappings with hierarchical process and propose two versions of minimax inequalities in topological vector spaces settings. As applications, we discuss the existent results of solutions for set equilibrium problems. Some examples are given to illustrate the established results.

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 Weak KKM set-valued mappings in hyperconvex metric spaces

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 157-167
Author(s):  
Ravi Agarwal ◽  
Mircea Balaj ◽  
Donal O’Regan
Keyword(s):  
Metric Spaces ◽  
Variational Inequality Problem ◽  
Strong Solutions ◽  
Vector Spaces ◽  
Minimax Inequalities ◽  
Topological Vector Spaces ◽  
Set Valued Mapping ◽  
General Variational Inequality ◽  
General Variational Inequality Problem ◽  
Existence Criteria

In this paper, the concept of weak KKM set-valued mapping is extended from topological vector spaces to hyperconvex metric spaces. For these mappings we obtain several intersection theorems that prove to be useful in establishing existence criteria for weak and strong solutions of the general variational inequality problem and minimax inequalities.

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 Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
A. P. Farajzadeh ◽  
A. Amini-Harandi ◽  
D. O'Regan
Keyword(s):  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Vector Equilibrium Problems ◽  
Solution Sets ◽  
Topological Vector Spaces ◽  
Set Valued Mapping ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium

We first define upper sign continuity for a set-valued mapping and then we consider two types of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005).

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