Boundary Point Method and Mann-Dotson's Algorithm for Nonself Strict Pseudo-contractive Mappings in Uniformly Smooth Banach Spaces. (19th May 2019) - Marino, Giuseppe; Muglia, Luigi
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 = ∞ .