ON SCHAUDER CONJECTURE FOR SET-VALUED MAPPINGS AND QUASI-EQUILIBRIUM PROBLEM

ON SCHAUDER CONJECTURE FOR SET-VALUED MAPPINGS AND QUASI-EQUILIBRIUM PROBLEM

S. Ranjbar, A. Farajzadeh

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Abstract

In this paper, the Schauder conjecture for set-valued mappings is studied by using suitable conditions. Also, an existence theorem for a solution of quasi-equilibrium problem in the setting of topological vector spaces is provided.

Keywords

Equilibrium problem, Lower semicontinuity, Quasi-equilibrium problem, Topo- logical vector space.