A new iterative scheme for equilibrium problems, fixed point problems for nonexpansive mappings and maximal monotone operators

DOI10.1186/1687-1812-2012-27zbMath1475.47068OpenAlexW2008585481WikidataQ59271217 ScholiaQ59271217MaRDI QIDQ367395

Poom Kumam, Nawitcha Onjai-uea

Publication date: 16 September 2013

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2012-27

zbMATH Keywords

maximal monotone operatorsstrong convergenceiterative schemestrongly 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

Approximating iterations for nonexpansive and maximal monotone operators ⋮ Convergence theorems for maximal monotone operators, weak relatively nonexpansive mappings and equilibrium problems

Cites Work

• Strong convergence theorem for a generalized equilibrium problem and system of variational inequalities problem and infinite family of strict pseudo-contractions
• A new strong convergence theorem for equilibrium problems and fixed point problems in Banach spaces
• New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators
• A hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi-nonexpansive mappings for generalized mixed equilibrium and variational inequality problems
• Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces
• Approximation of common fixed points of a countable family of relatively nonexpansive mappings
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• Existence and Approximation of Fixed Points of Firmly Nonexpansive-Type Mappings in Banach Spaces
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
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