Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications

DOI10.1016/j.nahs.2010.05.002zbMath1292.47049OpenAlexW2029945528MaRDI QIDQ608373

Xin Zhang, Jinlong Kang, Yongfu Su

Publication date: 25 November 2010

Published in: Nonlinear Analysis. Hybrid Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nahs.2010.05.002

zbMATH Keywords

fixed pointvariational inequalityequilibrium problemmonotone mappingweak relatively nonexpansive mapping

Mathematics Subject Classification ID

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

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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 ⋮ Strong convergence theorems of quasi-\(\phi\)-asymptotically nonexpansive semi-groups in Banach spaces ⋮ Total quasi-\(\phi\)-asymptotically nonexpansive semigroups and strong convergence theorems in Banach spaces ⋮ Strong convergence theorems for nonlinear mappings, variational inequality problems and system of generalized mixed equilibrium problems ⋮ A new iterative scheme for countable families of weak relatively nonexpansive mappings and system of generalized mixed equilibrium problems ⋮ A modified Halpern-type iteration algorithm for totally quasi-\(\phi \)-asymptotically nonexpansive mappings with applications ⋮ Strong convergence theorems for countable families of asymptotically relatively nonexpansive mappings with applications ⋮ Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type ⋮ Hybrid iterative scheme for fixed point problem, infinite systems of equilibrium and variational inequality problems ⋮ The modified Mann type iterative algorithm for a countable family of totally quasi-\(\phi\)-asymptotically nonexpansive mappings by the hybrid generalized f-projection method ⋮ Parallel iterative methods for a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces ⋮ Strong convergence theorems for Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces ⋮ Strong convergence theorems for families of weak relatively nonexpansive mappings ⋮ A new hybrid algorithm for solving a system of generalized mixed equilibrium problems, solving a family of quasi-\(\varphi\)-asymptotically nonexpansive mappings, and obtaining common fixed points in Banach space ⋮ Strong Convergence Theorems for a Finite Family of Sequences of Nearly Nonexpansive Mappings in Hilbert Spaces ⋮ The hybrid projection algorithm for finding the common fixed points of nonexpansive mappings and the zeroes of maximal monotone operators in Banach spaces ⋮ Parallel and sequential hybrid methods for a finite family of asymptotically quasi \(\phi \)-nonexpansive mappings

Cites Work

• A strong convergence theorem for relatively nonexpansive mappings in a Banach space
• Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces
• Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings
• Equilibrium programming using proximal-like algorithms
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• The fixed point theory of multi-valued mappings in topological vector spaces
• Existence and Approximation of Fixed Points of Firmly Nonexpansive-Type Mappings in Banach Spaces
• Inequalities in Banach spaces with applications
• Monotone Operators and the Proximal Point Algorithm
• Asymptotic Behavior of Relatively Nonexpansive Operators 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
• Nonlinear monotone operators and convex sets in Banach spaces
• Variational inequalities
• On the Maximality of Sums of Nonlinear Monotone Operators
• On uniformly convex functions
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