A coupled common fixed point theorem for a family of mappings

Abstract

In this paper we introduce the concept of coincidentally commuting pair in the context of coupled fixed point problems. It is established that an arbitrary family of mappings has a coupled common fixed point with two other functions under certain contractive inequality condition where two specific members of the family are assumed to be coincidentally commuting with these two functions respectively. The main result has certain corollaries. An example shows that the main theorem properly contains one of its corollaries.

Keywords

• coupled common fixed point
• coincidentally commuting mappings