Scholarlink

<p>We study a new Halpern-type iterative process enhanced with both inertial and error terms for the approximation of fixed points of pseudocontractions and zeros of monotone operators in real Hilbert spaces. Implementation of our algorithm is illustrated using numerical examples in real Hilbert spaces. It complements the results of Qihou (J Math Anal Appl 148:55–62, 1990) which are proved in compact, convex subset <i>C</i> of a real Hilbert space <i>H</i> and which is restricted to continuous pseudocontractions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T:C\rightarrow C\)</EquationSource> </InlineEquation> with finite set of fixed points <i>F</i>(<i>T</i>) and the results of Zegeye et al. (Nonlinear Anal 74:7304–7311, 2011) which are proved for Lipschitz pseudocontractions <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T:C\rightarrow C\)</EquationSource> </InlineEquation> where <i>C</i> is a nonempty closed convex subset of <i>H</i> and the interior of <i>F</i>(<i>T</i>) is nonempty. In all our examples, our algorithm enhanced with inertial and error terms is faster than the algorithms in Chidume and Zegeye (Proc Am Math Soc 132(3):831–840, 2004), Osilike et al. (J Appl Math Inform 31(3–4):565–575, 2013) and several other recent results which also yield strong convergence result for our class of maps. Extensions to double inertial schemes are also discussed.</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

Inertial terms enhanced iteration schemes for fixed points of pseudocontractions and zeros of monotone operators

  • 期刊论文

  • 发表日期：

    2026年2月16日

查看全文
  • E. E. Chima,
  • P. U. Nwokoro,
  • D. F. Agbebaku,
  • M. O. Osilike,
  • A. C. Onah,
  • O. U. Oguguo

摘要

We study a new Halpern-type iterative process enhanced with both inertial and error terms for the approximation of fixed points of pseudocontractions and zeros of monotone operators in real Hilbert spaces. Implementation of our algorithm is illustrated using numerical examples in real Hilbert spaces. It complements the results of Qihou (J Math Anal Appl 148:55–62, 1990) which are proved in compact, convex subset C of a real Hilbert space H and which is restricted to continuous pseudocontractions \(T:C\rightarrow C\) with finite set of fixed points F(T) and the results of Zegeye et al. (Nonlinear Anal 74:7304–7311, 2011) which are proved for Lipschitz pseudocontractions \(T:C\rightarrow C\) where C is a nonempty closed convex subset of H and the interior of F(T) is nonempty. In all our examples, our algorithm enhanced with inertial and error terms is faster than the algorithms in Chidume and Zegeye (Proc Am Math Soc 132(3):831–840, 2004), Osilike et al. (J Appl Math Inform 31(3–4):565–575, 2013) and several other recent results which also yield strong convergence result for our class of maps. Extensions to double inertial schemes are also discussed.