New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators

DOI10.1016/j.amc.2010.12.015zbMath1368.47086OpenAlexW2078558462MaRDI QIDQ628898

Yongfu Su, Mengqin Li, Hong Zhang

Publication date: 8 March 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.12.015

zbMATH Keywords

maximal monotone operatorCauchy sequencegeneralized projectionmonotone hybrid algorithmhemi-relatively nonexpansive mapping

Mathematics Subject Classification ID

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

Related Items

New construction and proof techniques of projection algorithm for countable maximal monotone mappings and weakly relatively non-expansive mappings in a Banach space ⋮ Parallel hybrid iterative methods for variational inequalities, equilibrium problems, and common fixed point problems ⋮ Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings ⋮ A new hybrid algorithm for \(\lambda\)-strict asymptotically pseudocontractions in 2-uniformly smooth Banach spaces ⋮ Convergence theorems based on the shrinking projection method for hemi-relatively nonexpansive mappings, variational inequalities and equilibrium problems ⋮ Strong convergence theorems for a finite family of \(\lambda_i\)-strict pseudocontractions in 2-uniformly smooth Banach spaces by metric projections ⋮ Strong convergence theorems for finite families of pseudomonotone equilibrium and fixed point problems in Banach spaces ⋮ Parallel and sequential hybrid methods for a finite family of asymptotically quasi \(\phi \)-nonexpansive mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A strong convergence theorem for relatively nonexpansive mappings in a Banach space
• Monotone CQ iteration processes for nonexpansive semigroups and maximal monotone operators
• Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Strong convergence of the CQ method for fixed point iteration processes
• Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups
• Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
• Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization
• Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• On the Maximality of Sums of Nonlinear Monotone Operators

This page was built for publication: New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators