Common fixed points for alpha-psi-phi-contractions in generalized metric spaces

Abstract

We establish some common fixed point theorems for mappings satisfying an α-ψ-ϕcontractive condition in generalized metric spaces. Presented theorems extend and generalize manyexisting results in the literature.
 Erratum to “Common fixed points for α-ψ-φ-contractions in generalized metric spaces”
 In Example 1 of our paper [V. La Rosa, P. Vetro, Common fixed points for α-ψ-ϕcontractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19(1):43–54, 2014] a generalized metric has been assumed. Nevertheless some mistakes have appeared in the statement. The aim of this note is to correct this situation.

Common Fixed Point Results for GeneralizedαspContractive Mappings and Applications

“…16. Taking = 1 in definition we obtain an −admissible mapping defined in [27]. Taking = as the identity mapping on , we deduce the definition of −admissible mapping as in [28].…”

Pata-Type Fixed Point Results in bv(s)-Metric Spaces

“…In this section, we prove some common fixed point results for two self-mappings. Following [27], we introduce the notion of f − α-admissible mapping.…”

Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

“…In 1984, Khan et al introduced the concept of altering distance function [23]. A ϕ-function is the extension of altering distance function and has been worked by many authors, [24,27,34]. For instance, the concepts of (α, ψ)-type contractive and α-admissible mappings were introduced by Gopal et al [17], who also established some fixed point theorems for these mappings in complete Menger spaces.…”