Strong Convergence of an Iterative Method with Perturbed Mappings for Nonexpansive and Accretive Operators

DOI10.1080/01630560801998203zbMath1140.47050OpenAlexW2091583388MaRDI QIDQ3506286

Lu-Chuan Ceng, Hong-Kun Xu, Jen-Chih Yao

Publication date: 12 June 2008

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630560801998203

zbMATH Keywords

strong convergencenonexpansive mapping\(m\)-accretive operatoruniformly smooth Banach spaceweakly continuous duality mapiterative method with perturbed mapping

Mathematics Subject Classification ID

Nonlinear accretive operators, dissipative operators, etc. (47H06) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Perturbations of nonlinear operators (47H14)

Related Items (20)

Hybrid Viscosity Approximation Method for Zeros ofm-Accretive Operators in Banach Spaces ⋮ Relaxed and composite viscosity methods for variational inequalities, fixed points of nonexpansive mappings and zeros of accretive operators ⋮ Strong convergence of an iterative algorithm for nonself multimaps in Banach spaces ⋮ Composite iterative algorithms for variational inequality and fixed point problems in real smooth and uniformly convex Banach spaces ⋮ A new approximation method for common fixed points of a finite family of generalized asymptotically quasinonexpansive mappings in Banach spaces ⋮ Iterative methods for a class of variational inequalities in Hilbert spaces ⋮ System of variational inequalities and an accretive operator in Banach spaces ⋮ New algorithms for a class of accretive variational inequalities in Banach spaces ⋮ A general composite iterative algorithm for nonexpansive mappings in Hilbert spaces ⋮ Strong convergence for solving a general system of variational inequalities and fixed point problems in Banach spaces ⋮ Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems ⋮ Three-step Mann iterations for a general system of variational inequalities and an infinite family of nonexpansive mappings in Banach spaces ⋮ Mann-type viscosity approximation methods for multivalued variational inclusions with finitely many variational inequality constraints in Banach spaces ⋮ Hybrid and relaxed Mann iterations for general systems of variational inequalities and nonexpansive mappings ⋮ Strong convergence of composite iterative schemes for zeros of \(m\)-accretive operators in Banach spaces ⋮ Strong convergence of implicit viscosity approximation methods for pseudocontractive mappings in Banach spaces ⋮ Mann-type extragradient methods for general systems of variational inequalities with multivalued variational inclusion constraints in Banach spaces ⋮ Modified hybrid steepest-descent methods for general systems of variational inequalities with solutions to zeros of \(m\)-accretive operators in Banach spaces ⋮ Approximate solutions of variational inequalities on sets of common fixed points of a one-parameter semigroup of nonexpansive mappings ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Product formulas, nonlinear semigroups, and accretive operators
• An iterative approach to quadratic optimization
• Convergence of generalized proximal point algorithms
• Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings
• Convergence theorems for sequences of nonlinear operators in Banach spaces
• Construction of fixed points of nonlinear mappings in Hilbert space
• Strong convergence of an iterative method for nonexpansive and accretive operators
• Iterative Algorithms for Nonlinear Operators
• Fixed point theorems for asymptotically nonexpansive mappings
• Iterative solutions for zeros of accretive operators
• FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE
• The Mann process for perturbed \(m\)-accretive operators in Banach spaces

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