ON RELATION THEORETIC COMMON FIXED POINT THEOREMS FOR PAIR OF MAPPINGS ENDOWED WITH A WEAKLY CLOSED RELATION

Abstract

The purpose of this paper is to rst dene the notion of (ꞔ,Ɦ)-weakly closed relation, supported by non-trivial examples. Utilize this notion to common fixed point theorem for pair of mappings satisfying generalized contraction involving rational terms and auxiliary functions in the context of relation theoretic metric space, without imposing completeness of the space. Further, to guarantee the uniqueness of fixed point, we assume that the space X is R^s-directed. Additionally, examples with graphical representations are provided to validate the main results.