Strong convergence of modified Mann iterations for a countable family of nonexpansive mappings

DOI10.1016/j.na.2008.04.014zbMath1203.47072OpenAlexW1968723057MaRDI QIDQ1009625

Rattanaporn Wangkeeree, Somyot Plubtieng

Publication date: 2 April 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.04.014

zbMATH Keywords

accretive operatorstrong convergencefixed pointnonexpansive mappinguniformly smooth

Mathematics Subject Classification ID

Nonlinear accretive operators, dissipative operators, etc. (47H06) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

The subgradient extragradient method for approximation of fixed-point problem and modification of equilibrium problem ⋮ New methods with perturbations for non-expansive mappings in Hilbert spaces ⋮ Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces ⋮ Approximating solutions of the generalized modification of the system of equilibrium problems and fixed point problem of a nonexpansive mapping ⋮ Approximation of fixed points for nonexpansive semigroups in Hilbert spaces ⋮ STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE ⋮ Iterative Methods for Nonexpansive Mappings in Banach Spaces ⋮ Hybrid algorithms of nonexpansive semigroups for variational inequalities ⋮ Strong convergence of composite iterative schemes for a countable family of nonexpansive mappings in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Approximation of a zero point of accretive operator in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• Strong convergence to common fixed points of families of nonexpansive mappings
• Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces.
• Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
• Strong convergence of modified Mann iterations
• Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings
• Convergence to common fixed points of a finite family of nonexpansive mappings
• Viscosity approximation methods for nonexpansive mappings
• The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space
• Viscosity approximation methods for fixed-points problems
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• Strong convergence and certain control conditions for modified Mann iteration
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• Fixed points of nonexpanding maps
• Weak and strong convergence of solutions to accretive operator inclusions and applications

This page was built for publication: Strong convergence of modified Mann iterations for a countable family of nonexpansive mappings