Abstract
In this article, we aim to evaluate and merge the as-scattered-as-possible results in fixed point theory from a general framework. In particular, we considered a common fixed point theorem via extended Z-contraction with respect to ψ -simulation function over an auxiliary function ξ in the setting of b-metric space. We investigated both the existence and uniqueness of common fixed points of such mappings. We used an example to illustrate the main result observed. Our main results cover several existing results in the corresponding literature.
Highlights
Introduction and PreliminariesThe concept of fixed point first appeared in articles where solutions of differential equations were discussed, especially solutions of initial value problems
The Banach fixed point theorem in most sources is given as follows: each contraction in a complete metric spaces admits a unique fixed point
In this article, we focus on the notion of simulation function
Summary
The concept of fixed point first appeared in articles where solutions of differential equations were discussed, especially solutions of initial value problems Among all such pioneer results in differential equations, we can mention and underline the renowned paper of Liouville [1], and the distinguished paper of Picard [2]. The Banach fixed point theorem in most sources is given as follows: each contraction in a complete metric spaces admits a unique fixed point. This is a characterization of Banach’s original result, in the context of metric space, was given by Caccioppoli [4].
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