General alternative regularization methods for nonexpansive mappings in Hilbert spaces

DOI10.1186/1687-1812-2014-203zbMath1345.47056OpenAlexW2153581924WikidataQ59323202 ScholiaQ59323202MaRDI QIDQ286936

Songnian He, Caiping Yang

Publication date: 26 May 2016

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

Full work available at URL: https://doi.org/10.1186/1687-1812-2014-203

zbMATH Keywords

fixed pointnonexpansive mappingviscosity approximation methodgeneral alternative regularization methodstrong pseudo-contraction

Mathematics Subject Classification ID

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

Related Items (14)

An inertial Mann algorithm for nonexpansive mappings ⋮ Bounded perturbation resilience of the viscosity algorithm ⋮ General alternative regularization method for solving split equality common fixed point problem for quasi-pseudocontractive mappings in Hilbert spaces ⋮ A general alternative regularization method with line search technique for solving split equilibrium and fixed point problems in Hilbert spaces ⋮ Iterative method for solving split common fixed point problem of asymptotically demicontractive mappings in Hilbert spaces ⋮ Unnamed Item ⋮ Bounded perturbation resilience and superiorization techniques for a modified proximal gradient method ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Iterative algorithms for solving the split feasibility problem in Hilbert spaces ⋮ General alternative regularization methods for split equality common fixed-point problem ⋮ Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings ⋮ Convergence Theorems and Convergence Rates for the General Inertial Krasnosel’skiǐ–Mann Algorithm ⋮ General viscosity iterative approximation for solving unconstrained convex optimization problems

Cites Work

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• Solving the variational inequality problem defined on intersection of finite level sets
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• Strong convergence theorems for resolvents of accretive operators in Banach spaces
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• Geometry of Banach spaces. Selected topics
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Viscosity approximation methods for nonexpansive mappings
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Viscosity approximation methods for fixed-points problems
• Iterative Algorithms for Nonlinear Operators
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• Variational inequalities
• Fixed points of nonexpanding maps
• Mean Value Methods in Iteration

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