A large averaging modified implicit iterative scheme with errors for finite family of asymtotically φ-demicontractive mappings

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  • Austine E. Ofem1,
  • Donatus Igbokwe2,
  1. Department of Mathematics, University of Uyo, Uyo, Nigeria
  2. Department of Mathematics, Michael Okpara University of Agriculture, University of Agriculture, Umidke, Nigeria

Published in Issue 2025-11-09

How to Cite

A large averaging modified implicit iterative scheme with errors for finite family of asymtotically φ-demicontractive mappings. (2025). Communications in Nonlinear Analysis, 8(2). https://oiccpress.com/cna/article/view/17932

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Abstract

In this paper, a three-step implicit iteration process with errors is introduced  and  we prove strong convergence theorem of the new iterative scheme with some mild conditions on the real sequences to a common fixed point of finite family of asymptotically φ-demicontractive mappings defined on a closed convex subset of a Banach space. The new iterative scheme includes several well known explicit and implicit iterative schemes. The results in this paper generalize several strong convergence results in the literature.

Keywords

  • Fixed point,
  • Banach space,
  • Implicit iteration process,
  • asymptotically φ-demicontractive mappings. 2010 AMS Subject Classification: 47H09
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