International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 659-661

An application of KKM-map principle

A. Carbone

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

Received 4 February 1991; Revised 6 June 1991

Copyright © 1992 A. Carbone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).