Boundary Point Method and Mann-Dotson's Algorithm for Nonself Strict Pseudo-contractive Mappings in Uniformly Smooth Banach Spaces. (19th May 2019)

• Record Type: Journal Article
• Authors: Marino, Giuseppe; Muglia, Luigi
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 7(2019)
• Page Start: 844
• Page End: 865
• Publication Date: 2019-05-19
• Subjects: Boundary point method -- inward condition -- nonself mappings -- strict pseudo-contractive mappings; 47H05 -- 47H10 -- 65J05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1561470
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let C be a closed, convex and nonempty subset of a q -uniformly smooth Banach space X. LetT : C → X be ak − strict pseducontractive inward mapping. We consider the boundary point maph C, T : C → ℝ depending on C and T defined byh C, T ( x ) = max { λ ∈ [ 0, 1 ] : [ ( 1 − λ ) x + λ T x ] ∈ C }, for allx ∈ C . Then for a suitable step-by-step construction of the control coefficients( α n ) n ∈ ℕ by using the functionh C, T, we show the convergence of the Mann-Dotson algorithm to a fixed point of T . We obtain strong convergence if∑ n α n < ∞ and weak convergence if∑ n α n = ∞ .