Fixed Points of Converse Commuting Mappings Using an Implicit Relation

Abstract

Abstract. In the present paper, we utilize the notion of converse commuting mappings due to Lü [On common fixed points for converse commuting self-maps on a metric spaces, Acta. Anal. Funct. Appl. 4(3) (2002), 226-228] and prove a common fixed point theorem in Menger space using an implicit relation. We also give an illustrative example to support our main result.

Some common fixed point theorems for converse commuting mappings via implicit relation

“…In 2002, Lü [12] presented the notion of the converse commuting mappings and established some fixed point theorems for single-valued mappings in metric spaces (also see [13,26]). Recently, Pathak and Verma [20,21], Chugh et al [7], Chauhan and Sapher [6], Chauhan et al [3] and Wang and Zhu [32] proved some interesting common fixed point theorems for converse commuting mappings in different settings.…”

Common Fixed Point Theorems for Conversely Commuting Mappings Using Implicit Relations

“…In 2002, Lü [10] presented the concept of the converse commuting mappings as a reverse process of weakly compatible mappings and proved common fixed point theorems for single-valued mappings in metric spaces (also see [11]). Recently, Pathak and Verma [12,13], Chugh et al [14], and Chauhan et al [15] proved some interesting common fixed point theorems for converse commuting mappings.…”