A Unique Common Fixed Point for an Infinity of Set-Valued Maps

Abstract

The main purpose of this paper is to establish some common fixed point theorems for single and set-valued maps in complete metric spaces, under contractive conditions by using minimal type commutativity and without continuity. These theorems generalize, extend and improve the result due to Elamrani and Mehdaoui ([2]) and others. Also, common fixed point theorems in metric spaces under strict contractive conditions are given.

Keywords

• complete metric space
• compatible and δ-compatible maps
• weakly compatible maps
• common fixed point