Coincidence and fixed points for compatible and relatively nonexpansive maps

Abstract

The concept of relatively nonexpansive maps is introduced. Fixed point and coincidence results for families of four self maps of metric spaces are obtained. Non-continuous compatible and relatively nonexpansive maps on star-shaped compact subsets of normed linear spaces are highlighted, and two theorems of Dotson are generalized.

Keywords

• relatively nonexpansive and compatible maps
• coincidence points.