INCLUSION AND INTERSECTION THEOREMS WITH APPLICATIONS IN EQUILIBRIUM THEORY IN G-CONVEX SPACES

Title & Authors
INCLUSION AND INTERSECTION THEOREMS WITH APPLICATIONS IN EQUILIBRIUM THEORY IN G-CONVEX SPACES
Balaj, Mircea; O'Regan, Donal;

Abstract
In this paper we obtain a very general theorem of $\small{\rho}$-compatibility for three multivalued mappings, one of them from the class $\small{\mathfrak{B}}$. More exactly, we show that given a G-convex space Y, two topological spaces X and Z, a (binary) relation $\small{\rho}$ on $\small{2^Z}$ and three mappings P : X $\small{\multimap}$ Z, Q : Y $\small{\multimap}$ Z and $\small{T\;{\in}\;\mathfrak{B}}$(Y,X) satisfying a set of conditions we can find ($\small{\widetilde{x},\;\widetilde{y}}$) $\small{{\in}}$ $\small{X\;{\times}\;Y}$ such that $\small{\widetilde{x}\;{\in}\;T(\widetilde{y})}$ and $\small{P(\widetilde{x}){\rho}\;Q(\widetilde{y})}$. Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.
Keywords
G-convex space;the better admissible class;fixed point;equilibrium problems;
Language
English
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