Exploring \(\mathfrak{F}\)-Khan-Contraction with Mann's Iterative Scheme in Convex \(S_b\)-Metric Spaces

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DOI: https://doi.org/10.28924/2291-8639-23-2025-302
Published: Nov 28, 2025
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Anas A. Hijab, Ahmad Aloqaily, Nabil Mlaiki, Exploring \(\mathfrak{F}\)-Khan-Contraction with Mann's Iterative Scheme in Convex \(S_b\)-Metric Spaces, Int. J. Anal. Appl., 23 (2025), 302.

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Anas A. Hijab, Ahmad Aloqaily, Nabil Mlaiki

Abstract

This manuscript presents the concept of Sb metric space for Mann’s iteration scheme, which extends the notion of b-metric, Gb-metric and S-metric spaces, respectively. We begin by introducing some improved and interesting properties, specifically regarding the concepts of symmetric and nonsymmetric within the context of Sb-metric space provided by examples. Additionally, we expand the notation of convex Sb-metric space through a convex Mann’s iteration algorithm. Furthermore, we display numerous outcomes of this new type of notion in the literature, with a particular focus on rational-Khan contractions and Wardowski-type contractions. The aim is to establish fixed-point results, accompanied by examples that clarify our findings. Finally, we provide applications to mixed Volterra-Fredholm integral and polynomial equations to support our theorems.

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