Regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in Banach spaces

DOI10.1186/1687-1812-2011-52zbMath1315.47067OpenAlexW2145449104WikidataQ59268592 ScholiaQ59268592MaRDI QIDQ362611

Truong Minh Tuyen, Jong Kyu Kim

Publication date: 22 August 2013

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

Full work available at URL: https://doi.org/10.1186/1687-1812-2011-52

zbMATH Keywords

mappingregularizationBanach spaceaccretive operatorssunny nonexpansive retractionuniformly smooth and uniformly convexweak sequential continuous

Mathematics Subject Classification ID

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

Related Items

Unnamed Item ⋮ Solution sensitivity of generalized nonlinear parametric \((A, \eta, m)\)-proximal operator system of equations in Hilbert spaces ⋮ Convergence rates in regularization for a system of nonlinear ill-posed equations with \(m\)-accretive operators ⋮ On solutions of inclusion problems and fixed point problems ⋮ A new iterative method for the set of solutions of equilibrium problems and of operator equations with inverse-strongly monotone mappings ⋮ Approximation common zero of two accretive operators in Banach spaces ⋮ Parallel iterative methods for a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces ⋮ A modified infeasible homotopy algorithm for computing fixed point in general non-convex set ⋮ Unnamed Item ⋮ Viscosity approximation method with Meir-Keeler contractions for common zero of accretive operators in Banach spaces ⋮ Strong Convergence Theorems for a Finite Family of Sequences of Nearly Nonexpansive Mappings in Hilbert Spaces

Cites Work

• A regularization method for the proximal point algorithm
• On the stability of iterative approximations to fixed points of nonexpansive mappings
• A note on a paper ``A regularization method for the proximal point algorithm
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Strong convergence theorems for nonexpansive nonself-mappings without boundary conditions
• Strong convergence of an iterative method for nonexpansive and accretive operators
• Nonlinear Ill-posed Problems of Monotone Type
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• On the moduli of convexity and smoothness
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Combining The Proximal Algorithm And Tikhonov Regularization
• Demiclosedness principle and asymptotic behavior for nonexpansive mappings in metric spaces