Fixed Point Theorems for Operators with Certain Condition in p-Uniformly Convex Metric Spaces

Knefati M., KARAKAYA V.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.43, no.16, pp.1884-1900, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 16
  • Publication Date: 2022
  • Doi Number: 10.1080/01630563.2022.2141256
  • Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.1884-1900
  • Keywords: Condition (D), Delta-convergence, JK-iteration process, p-uniformly convex metric space, strong convergence, ASYMPTOTIC-BEHAVIOR, CONVERGENCE
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, firstly, we extend the nonlinear Lebesgue spaces from the setting of Hadamard spaces to the setting of p-uniformly convex metric spaces. Afterward, we establish some Delta-convergence and strong convergence theorems for a recently introduced class of generalized nonexpansive mappings in the setting of p-uniformly convex metric spaces. Furthermore, we employ the newly introduced JK-iteration process to approximate the fixed points of this class. Finally, we construct new examples of this class of mappings in the context of p-uniformly convex metric spaces.