Fixed points of weakly compatible mappings satisfying generalized $\varphi$-weak contractions

Abstract

In this paper, utilizing the notion of the common limit in the range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a varphi-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend and generalize well-known results on the topic in the literature.