Approximation of fixed points for a new class of generalized non-expansivmappings in Banach spaces

Abdeljawad T., Karaca N., YILDIRIM İ., Mukheimer A.

AIMS Mathematics, vol.9, no.5, pp.11958-11974, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.3934/math.2024584
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.11958-11974
  • Keywords: fixed point, generalized non-expansive mappings, uniformly convex Banach spacMathematics
  • Ataturk University Affiliated: Yes

Abstract

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition Bγ,µ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.