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

Valeriu Popa

doi:10.2478/amsil-2020-0004

Abstract

Abstract A general fixed point theorem for two pairs of absorbing mappings satisfying a new type of implicit relation ([37]), without weak compatibility in Gp -metric spaces is proved. As applications, new results for mappings satisfying contractive conditions of integral type and for ϕ-contractive mappings are obtained.

Highlights

Let (X, d) be a metric space and S, T be two self mappings of X
In [4], [9], [10], [20], [21] and in other papers, some fixed point theorems under various contractive conditions in partial metric spaces have been proved
We introduce the notion of absorbing mapping in Gp-metric spaces

Summary

Introduction

Let (X, d) be a metric space and S, T be two self mappings of X. Two pairs (A, S) and (B, T ) of self mappings on a metric space (X, d) are said to satisfy common (E.A)-property if there exist two sequences {xn} and {yn} in X such that lim n→∞. A pair (A, S) of self mappings on a metric space (X, d) is said to satisfy common limit range property with respect to S, denoted CLR(S)-property, if there exists a sequence {xn} in X such that for some t ∈ S (X). Two pairs (A, S) and (B, T ) of self mappings of a metric space (X, d) are said to satisfy common limit range property with respect to S and T , denoted CLR(S,T )- property, if there exist two sequences {xn} and {yn} in X such that lim Axn = lim Sxn = lim Byn = lim T yn = t, n→∞.

Preliminaries

Implicit relations

Main results

Applications