On Mann's method with viscosity for nonexpansive and nonspreading mappings in Hilbert spaces
type: Item
instance of: scholarly article
title: On Mann's method with viscosity for nonexpansive and nonspreading mappings in Hilbert spaces
zbMATH Open document ID: 1428.47025
DOI: 10.1155/2014/152530
author: Nawab Hussain
author: Giuseppe Marino
author: A. A. N. Abdou
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: In the setting of Hilbert spaces, inspired by \textit{S. Iemoto} and \textit{W. Takahashi} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e2082--e2089 (2009; Zbl 1239.47054)], we study a Mann's method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7021817
zbMATH Keywords: Mann iteration
zbMATH Keywords: viscosity approximation
zbMATH Keywords: fixed points
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: nonspreading mapping
zbMATH Keywords: nonspreading-average type mapping
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/152530
OpenAlex ID: W1964556505
Wikidata QID: Q59035534
cites work: Construction of fixed points of nonlinear mappings in Hilbert space
cites work: Halpern iteration for firmly type nonexpansive mappings
cites work: Q4163944
cites work: Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces
cites work: Weak and strong convergence theorems for nonspreading-type mappings in Hilbert spaces
cites work: Q3998720
cites work: A unified treatment of some iterative algorithms in signal processing and image reconstruction
cites work: Über die Methode sukzessiver Approximationen
cites work: Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space
cites work: Halpern's iteration in Banach spaces
cites work: Krasnoselski–Mann iteration for hierarchical fixed-point problems
cites work: Q3451285
cites work: Viscosity approximation methods for fixed-points problems
cites work: Moudafi's viscosity approximations with Meir--Keeler contractions
cites work: A general iterative method for nonexpansive mappings in Hilbert spaces
cites work: Viscosity approximation methods for nonexpansive mappings
cites work: Analytical and numerical treatment of Jungck-type iterative schemes
cites work: Q5495613
cites work: Stability of the Ishikawa iteration scheme with errors for two strictly hemicontractive operators in Banach spaces
cites work: Strong convergence for solving a general system of variational inequalities and fixed point problems in Banach spaces
cites work: Q3601250
cites work: An iterative method for finding common solutions of equilibrium and fixed point problems
cites work: Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert spaces
cites work: Iterative Algorithms for Nonlinear Operators
cites work: Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
cites work: Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces
cites work: A general iterative method for quasi-nonexpansive mappings in Hilbert space
cites work: Cyclic iterative method for strictly pseudononspreading in Hilbert space
description: scientific article; zbMATH DE number 7021817