A Note on the Mann Iteration for k-Strict Pseudocontractions in Banach Spaces. (2nd January 2017)

• Record Type: Journal Article
• Authors: Sipoş, Andrei
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 1(2017)
• Page Start: 80
• Page End: 90
• Publication Date: 2017-01-02
• Subjects: Banach spaces -- effective rates of asymptotic regularity -- Mann iteration -- proof mining -- uniformly smooth Banach spaces; 47J25 -- 47H09; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1218894
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We show that a variant of a previously defined function can be used to characterize 2-uniform smoothness. We then obtain greatly simplified proofs of two convergence theorems in the literature using a generalization of a lemma of and the aforementioned characterization. We also more easily obtain rates of asymptotic regularity corresponding to the studied iterations. Finally, we derive a way to relate two constants which are characteristic to 2-uniformly smooth spaces.