Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces

This paper investigates the approximation of fixed points for mappings that satisfy the enriched (C) condition using a modified iterative process in a Banach space framework. We first establish a weak convergence result and then derive strong convergence theorems under suitable assumptions. To illus...

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Main Authors: Doaa Filali, Fahad Maqbul Alamrani, Esmail Alshaban, Adel Alatawi, Amid Yousef Alanazi, Faizan Ahmad Khan
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/6/426
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author Doaa Filali
Fahad Maqbul Alamrani
Esmail Alshaban
Adel Alatawi
Amid Yousef Alanazi
Faizan Ahmad Khan
author_facet Doaa Filali
Fahad Maqbul Alamrani
Esmail Alshaban
Adel Alatawi
Amid Yousef Alanazi
Faizan Ahmad Khan
author_sort Doaa Filali
collection DOAJ
description This paper investigates the approximation of fixed points for mappings that satisfy the enriched (C) condition using a modified iterative process in a Banach space framework. We first establish a weak convergence result and then derive strong convergence theorems under suitable assumptions. To illustrate the applicability of our findings, we present a numerical example involving mappings that satisfy the enriched (C) condition but not the standard (C) condition. Additionally, numerical computations and graphical representations demonstrate that the proposed iterative process achieves a faster convergence rate compared to several existing methods. As a practical application, we introduce a projection based an iterative process for solving split feasibility problems (SFPs) in a Hilbert space setting. Our findings contribute to the ongoing development of iterative processes for solving optimization and feasibility problems in mathematical and applied sciences.
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institution Kabale University
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spelling doaj-art-92faa886036b4751a0f02842e7744b9b2025-08-20T03:26:15ZengMDPI AGAxioms2075-16802025-05-0114642610.3390/axioms14060426Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach SpacesDoaa Filali0Fahad Maqbul Alamrani1Esmail Alshaban2Adel Alatawi3Amid Yousef Alanazi4Faizan Ahmad Khan5Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaThis paper investigates the approximation of fixed points for mappings that satisfy the enriched (C) condition using a modified iterative process in a Banach space framework. We first establish a weak convergence result and then derive strong convergence theorems under suitable assumptions. To illustrate the applicability of our findings, we present a numerical example involving mappings that satisfy the enriched (C) condition but not the standard (C) condition. Additionally, numerical computations and graphical representations demonstrate that the proposed iterative process achieves a faster convergence rate compared to several existing methods. As a practical application, we introduce a projection based an iterative process for solving split feasibility problems (SFPs) in a Hilbert space setting. Our findings contribute to the ongoing development of iterative processes for solving optimization and feasibility problems in mathematical and applied sciences.https://www.mdpi.com/2075-1680/14/6/426iterative processenriched condition (C)Banach spacesfixed pointsplit feasibility problem
spellingShingle Doaa Filali
Fahad Maqbul Alamrani
Esmail Alshaban
Adel Alatawi
Amid Yousef Alanazi
Faizan Ahmad Khan
Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces
Axioms
iterative process
enriched condition (C)
Banach spaces
fixed point
split feasibility problem
title Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces
title_full Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces
title_fullStr Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces
title_full_unstemmed Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces
title_short Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces
title_sort fixed point approximation for enriched suzuki nonexpansive mappings in banach spaces
topic iterative process
enriched condition (C)
Banach spaces
fixed point
split feasibility problem
url https://www.mdpi.com/2075-1680/14/6/426
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