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

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.