Common Fixed Points of Weakly Reciprocally Continuous Maps using a Gauge Function

Abstract

The aim of the present paper is to obtain a common fixed point theorem by employing the recently introduced notion of weak reciprocal continuity. We demonstrate that weak reciprocal continuity ensures the existence of fixed points under contractive conditions which otherwise do not ensure the existence of fixed points. Our result generalize and extend several well-known fixed point theorems due to Boyd and Wong (1969), Jungck(1976), Pant (1994) and Pathak et al (1997).

Keywords: Fixed point theorems, compatible maps, A-compatible maps, T-compatible maps, reciprocal continuity, weak reciprocal continuity