Abstract
Abstract In this paper, we characterize α-ψ contractive mappings in the setting of quasi-metric spaces and investigate the existence and uniqueness of a fixed point of such mappings. We notice that by using our result some fixed-point theorems in the context of G-metric space can be deduced. MSC:46T99, 47H10, 54H25, 46J10.
Highlights
Introduction and preliminariesLet be the family of functions ψ : [, ∞) → [, ∞) satisfying the following conditions:(ψ ) ψ is nondecreasing; (ψ ) +∞ n= ψ n (t) < ∞ for all t >, where ψn is the nth iterate of ψ.These functions are known in the literature as (c)-comparison functions
Where ψn is the nth iterate of ψ
Taking ( . ) and ( . ) into account, we find that d(xn+, xn) = d(Txn, Txn– ) ≤ α(xn, xn– )d(Txn, Txn– ) ≤ ψ d(xn, xn– ), ( . )
Summary
Definition Let (X, d) be a quasi-metric space and {xn} be a sequence in X.
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