Abstract
The aim of this article is to discuss the convergence of iterative sequences of the Prešić type involving new classes of operators satisfying Prešić type Θ -contractive condition in the context of metric spaces. Some examples are also provided to show the significance of the investigation of finding fixed points. Some convergence results for a class of matrix difference equations will be derived as application.
Highlights
Introduction and PreliminariesBanach’s contraction principle [1] is one of the decisive results of fixed point theory
In 1965, Presic [2] generalized the famous Banach contraction principle and applied the obtained results to secure the convergence of a specific type of sequences
A mapping L: S ⟶ S is called a Θ-contraction if there exist some λ ∈ (0, 1) and a function Θ satisfying (Θ1)–(Θ3) such that
Summary
Banach’s contraction principle [1] is one of the decisive results of fixed point theory. It states that if we have a self mapping L on a complete metric space (S, σ) and a constant λ ∈ (0, 1) such that σ(La, Lb) ≤ λσ(a, b),. Let L: Sk ⟶ S be a mapping satisfying the following contractive condition:. Holds for all a∗, a/ ∈ S, with a∗ ≠ a/, the fixed point in S is unique. A mapping L: S ⟶ S is called a Θ-contraction if there exist some λ ∈ (0, 1) and a function Θ satisfying (Θ1)–(Θ3) such that. Let L: S ⟶ S be a Θ-contraction; L has a unique fixed point. E given results unify and generalize various existing results of the literature
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