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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MDPI AG
2025-05-01
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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. |
| format | Article |
| id | doaj-art-92faa886036b4751a0f02842e7744b9b |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| 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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