Operators with Property (E) as Concerns Numerical Analysis and Visualization. (17th August 2020)

• Record Type: Journal Article
• Authors: Usurelu, Gabriela Ioana; Bejenaru, Andreea; Postolache, Mihai
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 11(2020)
• Page Start: 1398
• Page End: 1419
• Publication Date: 2020-08-17
• Subjects: Convergence analysis -- Garcia-Falset mapping -- Opial's property -- three-step iteration; 47H10 -- 54H25 -- 37C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1775252
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we study a Thakur three-step iterative process in the new context of generalized nonexpansive mappings enriched with property ( E ). A uniformly convex Banach space is used as underlying setting for our approach. In order to emphasize our results we offer an example of a mapping on R 2 endowed with property ( E ) that exceeds the well known class of Suzuki mappings. By connecting the Thakur iterative process (and many other iterations) with this example, we perform a comparative numerical experiment. This brings to light a new method that allows the visualization of some convergence behaviors.