Abstract
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 in Gpmetric spaces. In the last part of the paper, some fixed point results for mappings satisfying contractive conditions of integral type and for ⱷ-contractive mappings are obtained.
Highlights
Let (X, d) be a metric space and S, T be self mappings of X
We introduce a new type of common limit range property
In [4, 9, 10, 21, 22], some fixed point theorems under various contractive conditions in partial metric spaces have been proved
Summary
Let (X, d) be a metric space and S, T be self mappings of X. A pair (A, S) of self mappings of a metric space (X, d) is said to satisfy the common limit range property with respect to S (shortly CLR(S)-property), if there exists a sequence {xn} in X such that limn→∞ Axn = limn→∞ Sxn = t for some t ∈ S(X). Two pairs (A, S) and (B, T ) of self mappings in a metric space (X, d) are said to satisfy common limit range property with respect to S and T (shortly CLR(S,T )-property), if there exist two sequences {xn} and {yn} in X such that limn→∞ Axn = limn→∞ Sxn = limn→∞ Byn = limn→∞ T yn = t for some t ∈ S(X) ∩ T (X).
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