Strong convergence theorems by the hybrid method for families of mappings in Banach spaces

DOI10.1016/j.na.2008.10.108zbMath1221.47119OpenAlexW1987892353MaRDI QIDQ1026034

Kazuya Shimoji, Kazuhide Nakajo, Takahashi, Wataru

Publication date: 24 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.2008.10.108

zbMATH Keywords

strong convergencemonotone operatorconvex feasibility problemhybrid methodproximal point algorithm

Mathematics Subject Classification ID

Numerical methods based on necessary conditions (49M05) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25)

Related Items

Hybrid proximal point algorithm and applications to equilibrium problems and convex programming ⋮ The problem of image recovery by the metric projections in Banach spaces ⋮ Strong convergence theorems of common fixed points for a family of quasi-\(\varphi\)-nonexpansive mappings ⋮ Strong convergence to a solution of a variational inequality problem in Banach spaces ⋮ Fixed point solutions for variational inequalities in image restoration over \(q\)-uniformly smooth Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximating fixed points of infinite nonexpansive mappings by the hybrid method
• Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces
• Characterization of the subdifferentials of convex functions
• Nonlinear maximal monotone operators in Banach space
• On the maximal monotonicity of subdifferential mappings
• Inequalities in Banach spaces with applications
• A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces