Variants of R-weakly commuting mappings satisfying a weak contraction

Abstract

In this paper, first we prove a common fixed point theorem for pairs of weakly compatible mappings satisfying a generalized φ-weak contraction condition that involves cubic terms of metric functions. Secondly, we prove some results using different variants of R-weakly commuting mappings. At the end, we give an application in support of our results.

Common fixed point results for a generalized ( ψ, φ )-rational contraction

“…Besides, many researchers have studied such types of contractive conditions and have been proved some interesting fixed point results for (ψ, φ)-contractive mappings, see [2,4,5,3,7,8,10,11,9,19,12,13,16,15,17,14,18,20] and references therein. Now, we establish two common fixed theorems for two mappings satisfying a generalized (ψ, φ)-rational contractive condition in a complete metric space.…”