Convergence of composite iterative methods for finding zeros of accretive operators

DOI10.1016/j.na.2009.01.010zbMath1219.47118OpenAlexW2048583956MaRDI QIDQ1030067

Jong Soo Jung

Publication date: 1 July 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.01.010

zbMATH Keywords

strong convergencezerosresolventsaccretive operatorsuniformly Gâteaux differentiable normstrictly convexreflexiveviscosity approximation methodscomposite iterative schemes

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Numerical methods based on necessary conditions (49M05) Nonlinear accretive operators, dissipative operators, etc. (47H06) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10)

Related Items

Relaxed and composite viscosity methods for variational inequalities, fixed points of nonexpansive mappings and zeros of accretive operators ⋮ Some results on Rockafellar-type iterative algorithms for zeros of accretive operators ⋮ Convergence of a hybrid viscosity approximation method for finding zeros of \(m\)-accretive operators ⋮ System of variational inequalities and an accretive operator in Banach spaces ⋮ Iterative approximation for a zero of accretive operator and fixed points problems in Banach space ⋮ Strong convergence of a modified viscosity iteration for common zeros of a finite family of accretive mappings ⋮ Approximation common zero of two accretive operators in Banach spaces ⋮ Iterative algorithms with errors for zero points of \(m\)-accretive operators ⋮ Strong convergence of a new composite iterative method for equilibrium problems and fixed point problems ⋮ Implicit and explicit iterative methods for systems of variational inequalities and zeros of accretive operators ⋮ Viscosity approximation methods for two accretive operators in Banach spaces ⋮ Hybrid extragradient methods for finding zeros of accretive operators and solving variational inequality and fixed point problems in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strong convergence theorems on an iterative method for a family of finite nonexpansive mappings
• Approximation of a zero point of accretive operator in Banach spaces
• Convergence on composite iterative schemes for nonexpansive mappings in Banach spaces
• Viscosity approximation method for accretive operator in Banach space
• Solving variational inequalities involving nonexpansive type mappings
• Strong convergence of composite iterative schemes for zeros of \(m\)-accretive operators in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Dual convergence theorems for the infinite products of resolvents in Banach spaces
• Geometry of Banach spaces. Selected topics
• Produits infinis de resolvantes
• Strong convergence of modified Mann iterations
• Approximating solutions of maximal monotone operators in Hilbert spaces
• Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
• Some theorems on weakly contractive maps.
• 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
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• Viscosity approximation fixed points for nonexpansive and \(m\)-accretive operators
• Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces
• Iterative schemes with some control conditions for a family of finite nonexpansive mappings in Banach spaces
• Viscosity methods for zeroes of accretive operators
• Approximating zero points of accretive operators with compact domains in general Banach spaces
• Strong convergence of an iterative method for nonexpansive and accretive operators
• CONVERGENCE OF APPROXIMATING PATHS TO SOLUTIONS OF VARIATIONAL INEQUALITIES INVOLVING NON-LIPSCHITZIAN MAPPINGS
• On the Fixed-Point Theory for Local k-Pseudocontractions
• Almost convergence of the infinite product of resolvents in Banach spaces
• Iterative solutions for zeros of accretive operators
• On the asymptotic behavior of infinite products of resolvents in Banach spaces
• The Mann process for perturbed \(m\)-accretive operators in Banach spaces
• Extension of subgradient techniques for nonsmooth optimization in Banach spaces