An application of KKM-map principle

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:C→X a continuous function, g:C→C continuous, onto and almost quasi-convex. Assume that C has a nonempty compact convex subset D such that the setA={y∈C:‖g(x)−f(y)‖≥‖g(y)−f(y)‖ for all x∈D}is compact.

Keywords

• almost quasi-convex functions
• fixed points
• coincidence points.