On the error estimation and \(T\)-stability of the Mann iteration

DOI10.1016/j.cam.2014.08.031zbMath1300.65036OpenAlexW2010034122MaRDI QIDQ458176

Ștefan Mărușter, Laura Măruşter

Publication date: 7 October 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.08.031

zbMATH Keywords

strong convergencenumerical exampleserror estimationnonlinear operator equationMann iteration\(T\)-stabilitystrongly demicontractive mapping

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (7)

Local convergence of Exquerro-Hernandez method ⋮ Unnamed Item ⋮ Stability and convergence rate of Jungck-type iterations for a pair of strongly demicontractive mappings in Hilbert spaces ⋮ Exponential inequalities for Mann’s stochastic algorithm ⋮ Weak \(w^{2}\)-stability and data dependence of Mann iteration method in Hilbert spaces ⋮ On the error estimation and T-stability of the Ishikawa iteration for strongly demicontractive mappings ⋮ A note on the error estimation of the Mann iteration

Cites Work

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• Strong convergence of the mann iteration for -demicontractive mappings
• On the strong convergence of an algorithm about firmly pseudo-demicontractive mappings for the split common fixed-point problem
• Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces
• Iterative approximation of fixed points
• \(T\)-stability of Picard iteration in metric spaces
• Construction of common fixed points of a countable family of \(\lambda\)-demicontractive mappings in arbitrary Banach spaces
• Convergence of the Mann iteration algorithm for a class of pseudocontractive mappings
• Some combined relations between contractive mappings, Kannan mappings, reasonable expansive mappings, and \(T\)-stability
• An example concerning fixed points
• On the Mann iteration process in a Hilbert space
• On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings
• Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators
• Sur Le Calcul Des Zeros D'un Operateur Discontinu Par Iteration
• The Solution by Iteration of Nonlinear Equations in Hilbert Spaces
• An Iterative Process for Nonlinear Monotonic Nonexpansive Operators in Hilbert Space
• Approximation of fixed points of a strictly pseudocontractive mapping
• The Round‐off Stability of Iterations

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