International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 659-661
doi:10.1155/S0161171292000875

An application of KKM-map principle

A. Carbone

Dipartimento di Matematica, Universitá degli studi della Calabria, Arcavacata di Rende (Cosenza) 87036, Italy

Abstract

The following theorem is proved and several fixed point theorems and coincidence theorems are derived as corollaries. Let C be a nonempty convex subset of a normed linear space X, f:CX a continuous function, g:CC continuous, onto and almost quasi-convex. Assume that C has a nonempty compact convex subset D such that the setA={yC:g(x)f(y)g(y)f(y)forallxD}is compact.Then there is a point y0C such that g(y0)f(y0)=d(f(y0),C).