ON SOME COMMON FIXED POINT RESULTS OF G\'{O}RNICKI-TYPE MAPPINGS

Abstract

In this article, we focus on a pair of G\'{o}rnicki-type mappings $T_1,T_2\in X^X$, $(X,d)$ being a metric space, satisfying $d(T_1x,T_2y) \leq M [d(x, T_2y) + d(y, T_1x) + d(x, y)]$ for all $x,y \in X$ where $0\le M<1$. The significance of such mappings lies in their broader class compared to contraction and nonexpansive mappings. Our main focus is on the common fixed point(s) of this pair of G\'{o}rnicki-type mappings. Specifically, we establish conditions under which a couple of mappings share fixed points satisfying the aforementioned inequality. Additionally, we provide several non-trivial examples to validate our results.