Strong convergence of averaged iteration for asymptotitcally non-expansive non-self mappings

Modified Halpern Iteration of Asymptotically Non-Expansive Mappings

modified halpern iteration of asymptotically non-expansive mappings

Ergodic Theorem and Strong Convergence of Averaged Approximants for Non-lipschitzian Mappings in Banach Spaces

Let C be a bounded closed convex subset of a uniformly convex Banach space X and let T be an asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we first provide a ergodic retraction theorem and a mean ergodic convergence theorem. Using this result, we show that the set F (T ) of fixed points of T is a sunny, nonexpansive retract of C if the norm of X is u...

Strong Convergence of CQ Iteration for Asymptotically Nonexpansive Mappings

Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

Strong convergence of the Mann iteration for α-demicontractive mappings

The paper deals with strong convergence properties of the Mann iteration. A new class of demicontractive mappings (called α-demicontractive) is introduced for which the strong convergence of the computed sequence is assured. The paper presents also an overview of relevant contributions of the last two decades, concerning strong convergence for Mann-type iteration of demicontractive mappings.