Scholarlink

<p>In this paper, we introduce a new four-step iterative process for approximating fixed points of generalized <i>α</i>-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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>I</mi> <mo>−</mo> <msub> <mi>P</mi> <mi>T</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$I - P_{T}$</EquationSource> </InlineEquation>. Unlike contraction-based approaches, the stability of the process is analyzed directly within the generalized <i>α</i>-nonexpansive framework, demonstrating robustness under small perturbations. A numerical experiment in <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{R}^{2}$</EquationSource> </InlineEquation> 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月16日

查看全文
  • Makbule Kaplan Özekes

摘要

In this paper, we introduce a new four-step iterative process for approximating fixed points of generalized α-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 − P T $I - P_{T}$ . Unlike contraction-based approaches, the stability of the process is analyzed directly within the generalized α-nonexpansive framework, demonstrating robustness under small perturbations. A numerical experiment in R 2 $\mathbb{R}^{2}$ 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.