Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property

Abstract

The purpose of this paper is to prove a general fixed point theorem for mappings involving almost altering distances and satisfying a new type of common limit range property which generalize the results from Theorem 2.9 [19]. In the last part of the paper, as applications, some fixed point results for mappings satisfying contractive conditions of integral type for almost contractive mappings for φcontractive mappings and (ψ, φ)-weak contractive mappings in metric spaces are obtained.

A General Fixed Point Theorem for Two Pairs of Absorbing Mappings in Gp -Metric Spaces

“…Quite recently, the present author introduced in [37] a new type of common limit range property. Definition 1.6 ( [37]). Let A, S and T be self mappings of a metric space (X, d).…”

Common Fixed Points Theorem for Four Mappings on Metric Space Satisfying Contractive Conditions of Integral Type Jigmi Dorjee Bhutia and Kalishankar Tiwary

“…Denote C(f, g) = {x : f x = gx} is the collection of all coincidence points of selfmaps f and g of a metric space X. Theorem 1.23. [22] Let (X, d) be a metric space and f, g, h, and T be self mappings of X satisfying the inequality…”

A fixed point theorem for mappings satisfying a new common range property

“…Some fixed point results for two pairs of mappings with theorems with CLR (S) and CLR (S,T) -properties are obtained in [4], [5], [6] and other papers. Quite recently, a new type of common limit range property is introduced in [11]. Definition 1.4.…”

“…Definition 1.4. [11] Let A , S and T be self mappings of a metric space (X,d). The pair (A,S) is said to satisfy a common limit range property with respect to T, denoted by CLR (A,S,)T -property if there exist a sequence x n such that lim n−→∞ Ax n = lim n−→∞ Sx n = u S(X) ∩ T(X) Remark 1.1.…”