On a Three-Step Iteration Process for Suzuki Mappings with Qualitative Study. (10th June 2020)

• Record Type: Journal Article
• Authors: Maniu, Georgeta
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 8(2020)
• Page Start: 929
• Page End: 949
• Publication Date: 2020-06-10
• Subjects: Convergence -- data dependency -- stability -- Suzuki mapping -- three-step iteration; 47H10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1719415
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we extend the study of an iteration process introduced by Thakur-Thakur-Postolache [ J. Inequal. Appl., (2014), 147–155] from the class of nonexpansive operators to the more general class of Suzuki operators. We prove weak and strong convergence theorems regarding the iteration method for mappings satisfying the condition (C) of Suzuki in uniformly convex Banach spaces. We study the stability of this iteration process, and introduce a data dependency result for the subclass of contractive operators. An example illustrates the theoretical outcome.