Strong convergence of Mann's-type iterations for nonexpansive semigroups in general Banach spaces

DOI10.1016/j.na.2004.07.055zbMath1089.47052OpenAlexW1984765187MaRDI QIDQ1780770

Sachiko Atsushiba, Takahashi, Wataru

Publication date: 13 June 2005

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.2004.07.055

zbMATH Keywords

strong convergencenonexpansive mappingMann iterationnonexpansive semigroupfixed point approximation

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Viscosity approximation to a common solution of variational inequality problems and fixed point problems for Lipschitzian semigroup in Banach spaces ⋮ Convergence theorems of fixed points for Lipschitz pseudo-contractions in Hilbert spaces ⋮ Strong convergence theorems for a family non-expansive mappings and application to generalized mixed equilibrium problems systems ⋮ Approximating common fixed points of Lipschitzian semigroup in smooth Banach spaces ⋮ The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces

Cites Work

• Means on commutative semigroups and nonlinear ergodic theorems
• Mean ergodic theorems for semigroups of linear operators
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space
• Strong convergence to common fixed points of families of nonexpansive mappings
• A Nonlinear Ergodic Theorem for an Amenable Semigroup of Nonexpansive Mappings in a Hilbert Space
• Fixed point theorems and nonlinear ergodic theorems for nonlinear semigroups and their applications
• Approximating common fixed points of two nonexpansive mappings in Banach spaces
• Nonexpansive retractions and nonlinear ergodic theorems in Banach spaces
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• Mean Value Methods in Iteration
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