A new four-step iteration scheme for generalized α-nonexpansive multivalued mappings in Banach spaces

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dc.contributor.authorOzekes, Makbule Kaplan
dc.date.accessioned2026-04-25T14:20:18Z
dc.date.available2026-04-25T14:20:18Z
dc.date.issued2025
dc.departmentSinop Üniversitesi
dc.description.abstractIn this paper, we introduce a new four-step iterative process for approximating fixed points of generalized alpha-nonexpansive multivalued mappings in uniformly convex Banach spaces. The proposed iteration unifies and extends several classical schemes, including the Mann, Ishikawa and Noor processes, while preserving a simple computational structure. Strong and weak convergence theorems are established under mild conditions such as the Opial property and the demiclosedness of I-PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I - P_{T}$\end{document}. Unlike contraction-based approaches, the stability of the process is analyzed directly within the generalized alpha-nonexpansive framework, demonstrating robustness under small perturbations. A numerical experiment in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}<^>{2}$\end{document} illustrates the superior performance of the proposed algorithm, achieving faster residual decay and improved asymptotic regularity compared with existing methods. Both theoretical and numerical findings confirm the efficiency and stability of the scheme, suggesting promising applications in nonlinear analysis and optimization problems.
dc.identifier.doi10.1186/s13660-025-03422-3
dc.identifier.issn1029-242X
dc.identifier.issue1
dc.identifier.orcid0000-0002-7962-702X
dc.identifier.scopus2-s2.0-105027982563
dc.identifier.scopusqualityN/A
dc.identifier.urihttps://doi.org/10.1186/s13660-025-03422-3
dc.identifier.urihttps://hdl.handle.net/11486/8494
dc.identifier.volume2026
dc.identifier.wosWOS:001665640200001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorOzekes, Makbule Kaplan
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofJournal of Inequalities and Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20260420
dc.subjectFour-step iteration
dc.subjectMultivalued mapping
dc.subjectFixed point
dc.titleA new four-step iteration scheme for generalized α-nonexpansive multivalued mappings in Banach spaces
dc.typeArticle

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