Strong convergence theorems for a family of Lipschitz quasi-pseudo-contractions in Hilbert spaces

DOI10.1016/J.NA.2008.10.059zbMath1225.47123OpenAlexW2017935495MaRDI QIDQ1021702

Hai-Yun Zhou

Publication date: 9 June 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.2008.10.059

zbMATH Keywords

strong convergenceHilbert spacefamily of Lipschitz quasi-pseudo-contractionsmodified hybrid algorithm

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (6)

A new iteration method for variational inequalities on the set of common fixed points for a finite family of quasi-pseudocontractions in Hilbert spaces ⋮ Strong convergence theorems for equilibrium problems involving a family of nonexpansive mappings ⋮ Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions ⋮ A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces ⋮ Monotone hybrid projection algorithms for an infinitely countable family of Lipschitz generalized asymptotically quasi-nonexpansive mappings ⋮ Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings

Cites Work

• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• Approximation of a zero point of accretive operator in Banach spaces
• Convergence theorems of fixed points for \(\kappa \)-strict pseudo-contractions in Hilbert spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Strong convergence of modified Mann iterations
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Iterative methods for strict pseudo-contractions in Hilbert spaces
• Convergence theorems of a modified hybrid algorithm for a family of quasi-\(\varphi \)-asymptotically nonexpansive mappings
• Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces
• Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups
• Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
• Construction of fixed points of nonlinear mappings in Hilbert space
• FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE
• Mean Value Methods in Iteration

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