Generalized α-ψ-contractive type mappings of integral type and related fixed point theorems

Abstract

The aim of this paper is to introduce two classes of generalized α-ψ-contractive type mappings of integral type and to analyze the existence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude of relevant fixed point theorems of the existing literature. MSC: 54H25; 47H10; 54E50

On some fixed points of alpha-psi contractive mappings with rational expressions

“…For some other examples concerning the class of α-admissible mappings, we can see [2,3,7,9,19,24]. Definition 1.4.…”

On common fixed points for (α,ψ )-contractions and generalized cyclic contractions in b-metric-like spaces and consequences

“…Many papers dealing with above notion have been considered to prove some (common) fixed point results, for example see [1,3,6,9,17,18,19,20,21,24,26].…”

On common best proximity points for generalized α−ψ -proximal contractions

“…(a) S = T ; (b) A = B; (c) α(x, y) in a proper way like in [9]; (d) ψ(t) in a proper way like in [9]; (e) M (x, y) in a proper way.…”

“…In 2011, Sadiq Basha [17] stated some best proximity point theorems for proximal contractions. For some other results on best proximity points, see for example [1,3,5,6,7,8,9,10,11,12,13,14,15,16,18,19,21,22,23,24,25]. We recall some notations and definitions, which will be used in the sequel.…”