Fixed Point Theorems for Operators with Certain Condition in p-Uniformly Convex Metric Spaces. (22nd November 2022)

• Record Type: Journal Article
• Authors: Knefati, Mohammad; Karakaya, Vatan
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 16(2022)
• Page Start: 1884
• Page End: 1900
• Publication Date: 2022-11-22
• Subjects: Condition (D) -- Δ-convergence -- JK-iteration process -- p-uniformly convex metric space -- strong convergence; 47H09 -- 47H10 -- 49HJ20 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2141256
• Languages: English
• ISSNs: 0163-0563

Abstract

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 Δ-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.