Unified implicit common fixed point theorems under non-negative complex valued functions satisfying the identity of indiscernible

Abstract

In this paper, we consider a non-negative complex valued function satisfying the identity of indiscernible and utilize the same to prove some common fixed point theorems for two pairs of non-vacuously weakly compatible mappings satisfying an implicit relation having rational terms as its co-ordinates. Some illustrative examples are also given which demonstrate the validity of the hypotheses of our results. In process, a host of previously known results in the context of complex as well as real valued metric spaces are generalized and improved.

Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

“…Recently, Azam et al [3] introduced the concept of complex valued metric spaces which is relatively more general than metric spaces and also proved common fixed point theorems for two mappings satisfying certain rational inequalities. Since then, several papers have dealt with fixed point theory in complex valued metric spaces (see [2,4,5,16,14,22,21,18,19,17,20,23,14] and references cited therein).…”