Convergence theorems based on the shrinking projection method for hemi-relatively nonexpansive mappings, variational inequalities and equilibrium problems

DOI10.15352/bjma/1337014662zbMath1318.47085OpenAlexW2757267579MaRDI QIDQ437696

Mi Kwang Kang, Zi-Ming Wang, Yeol Je Cho

Publication date: 18 July 2012

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bjma/1337014662

zbMATH Keywords

variational inequalitiesBanach spaceequilibrium problemshrinking projection methodhemi-relatively nonexpansive mappings

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

Parallel hybrid iterative methods for variational inequalities, equilibrium problems, and common fixed point problems ⋮ Unnamed Item ⋮ Hybrid methods for a mixed equilibrium problem and fixed points of a countable family of multivalued nonexpansive mappings ⋮ Halpern-type iterative algorithm for an infinite family of relatively quasi-nonexpansive multivalued mappings and equilibrium problem in Banach spaces ⋮ Convergence to a common fixed point of a finite family of generalized asymptotically nonexpansive mappings

Cites Work

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• A strong convergence theorem for relatively nonexpansive mappings in a Banach space
• New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators
• Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings
• Strong convergence of shrinking projection methods for quasi-nonexpansive mappings and equilibrium problems
• Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces
• On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• On the existence of solutions of variational inequalities in Banach spaces
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Convergence theorems based on the shrinking projection method for variational inequality and equilibrium problems
• Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings
• Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces
• A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces
• Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• On the projection methods for fixed point problems
• Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• On Some Estimates for Projection Operator in Banach Space
• Fixed Points by a New Iteration Method
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• On the Maximality of Sums of Nonlinear Monotone Operators

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