Common fixed point theorems in symmetric spaces employing a new implicit function and common property (E.A)

Abstract

The aim of this paper is broadly two fold. Firstly, we define a new class of implicit function unifying a multitude of strict contractive conditions and utilize the same to prove a general common fixed point theorem for two pairs of weak compatible mappings satisfying common property $(E.A)$ when underlying space is not necessarily compact. Secondly, we show that common property $(E.A)$ relaxes the required containment of ranges of the involved mappings in common fixed point considerations up to two pairs of mappings.