Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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INCLUSION AND INTERSECTION THEOREMS WITH APPLICATIONS IN EQUILIBRIUM THEORY IN G-CONVEX SPACES

  • Balaj, Mircea (DEPARTMENT OF MATHEMATICS UNIVERSITY OF ORADEA) ;
  • O'Regan, Donal (DEPARTMENT OF MATHEMATICS NATIONAL UNIVERSITY OF IRELAND)
  • Received : 2009.01.12
  • Published : 2010.09.01
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Abstract

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

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