Approximating common fixed points of two nonexpansive mappings in Banach spaces

DOI10.1017/S0004972700031464zbMath0913.47047MaRDI QIDQ4397368

Takahashi, Wataru, Sachiko Atsushiba

Publication date: 7 July 1998

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Fréchet differentiableOpial's conditionuniformly convex Banach spacenonexpansive mappingsnonlinear ergodic theoryapproximating common fixed pointsiteration procedure of Mann's type

Mathematics Subject Classification ID

Numerical methods based on necessary conditions (49M05) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Mean convergence theorems using hybrid methods to find common fixed points for noncommutative nonlinear mappings in Hilbert spaces ⋮ Convergence theorems using Ishikawa iteration for finding common fixed points of demiclosed and 2-demiclosed mappings in Hilbert spaces ⋮ STRONG CONVERGENCE TO COMMON FIXED POINTS USING ISHIKAWA AND HYBRID METHODS FOR MEAN-DEMICLOSED MAPPINGS IN HILBERT SPACES ⋮ Ishikawa type mean convergence theorems for finding common fixed points of nonlinear mappings in Hilbert spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals ⋮ Strong convergence of Mann's-type iterations for nonexpansive semigroups in general Banach spaces ⋮ A weak convergence theorem for common fixed points of two nonlinear mappings in Hilbert spaces

Cites Work

• Weak convergence theorems for nonexpansive mappings in Banach spaces
• On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces
• Some geometric properties related to the fixed point theory for nonexpansive mappings
• Equivalent Norms and the Fixed Point Property for Nonexpansive Mappings
• Inequalities in Banach spaces with applications
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Mean Value Methods in Iteration