Asymptotic Behaviour of ϕ-Nonexpansive Sequences and Mappings in Banach Spaces. (19th May 2022)

• Record Type: Journal Article
• Authors: Djafari Rouhani, Behzad; Khatibzadeh, Hadi; Mohebbi, Vahid
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 7(2022)
• Page Start: 860
• Page End: 875
• Publication Date: 2022-05-19
• Subjects: Asymptotic behavior -- asymptotically regular sequence -- strong convergence -- weak convergence -- ϕ-nonexpansive sequence; Primary 47H25 -- 47H09 -- 47H10 -- 47J25. Secondary 37A30 -- 47H20 -- 47H30 -- 47H05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2066690
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce the notion of ϕ -nonexpansive sequences and maps in a Banach space E, and prove an ergodic theorem, a fixed point theorem, and some weak and strong convergence theorems for such sequences and maps in E, with rather mild assumptions on the Banach space E, weaker than those assumed by previous authors for nonexpansive maps. These results give a partial answer to the still open problem raised in 1981 by Djafari Rouhani for nonexpansive sequences in a Banach space.