A note on implicit and explicit Mann iterative processes for asymptotically \(\phi\)-strongly pseudocontractive mappings
type: Item
instance of: scholarly article
title: A note on implicit and explicit Mann iterative processes for asymptotically \(\phi\)-strongly pseudocontractive mappings
zbMATH Open document ID: 1366.47020
DOI: 10.1155/2012/912050
author: Luigi Muglia
author: Yonghong Yao
published in: Journal of Applied Mathematics
publication date: 2012-08-06T00:00:00Z
review text: Summary: We prove the equivalence and the strong convergence of an explicit Mann iterative process and a modified implicit iterative process for asymptotically \(\phi\)-strongly pseudocontractive mappings in a uniformly smooth Banach space.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 6063512
zbMATH Keywords: strong convergence
zbMATH Keywords: explicit Mann iterative process
zbMATH Keywords: modified implicit iterative process
zbMATH Keywords: asymptotically \(\phi\)-strongly pseudocontractive mappings
zbMATH Keywords: uniformly smooth Banach space
Wikidata QID: Q58906928
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/912050
OpenAlex ID: W1972083524
cites work: A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
cites work: NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
cites work: Iterative construction of fixed points of asymptotically nonexpansive mappings
cites work: Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space
cites work: Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces
cites work: Q3586231
cites work: Iterative approximation of fixed points for asymptotically strict pseudocontractive type mappings in the intermediate sense
cites work: Geometric properties of Banach spaces and nonlinear iterations
cites work: Asymptotically strict pseudocontractive mappings in the intermediate sense
cites work: Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings.
cites work: Zeros of accretive operators
cites work: Iterative solution of nonlinear equations of the \(\Phi\)-strongly accretive type
cites work: Q5185568
cites work: Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
cites work: Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings
cites work: On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings
cites work: The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings
cites work: Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively \(\Phi \)-pseudocontractive mappings without Lipschitzian assumptions
cites work: The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption
cites work: Equilibrium points for a system involving \(m\)-accretive operators
cites work: Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings.
cites work: Ishikawa and Mann iterative processes with error for nonlinear strongly accretive operator equations
cites work: Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces
cites work: Convergence theorem for zeros of generalized Lipschitz generalized phi-quasi-accretive operators
description: scientific article; zbMATH DE number 6063512