CONTINUOUS SELECTION THEOREM FOR phi_FC-MAPPINGS IN FC-SPACES AND ITS APPLICATIONS

Abstract

Three new concepts of better admissible class B_FC (Y,X), phi_FC-mappings and phi_FC -spaces are introduced. A continuous selection theorem for phi_FC-mappings in FC-spaces is obtained. By using the continuous selection theorem, a fixed point theorem involving B_FC (Y,Y) in phi_FC-spaces is proved. As applications, a quasi-equilibrium theorem and a generalized quasi-equilibrium theorem are proved.