A characterization of the convergence of Picard iteration to a fixed point for a continuous mapping and an application

DOI10.1016/J.AMC.2004.10.056zbMath1081.65048OpenAlexW1989965020MaRDI QIDQ2571977

Yanyan Li

Publication date: 14 November 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2004.10.056

zbMATH Keywords

convergencefixed pointIshikawa iterationPicard iterationnonexpansive mapcontinuous mapasymptotically regular propertymetric/normed spaceright continuous function

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (1)

Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications

Cites Work

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• Convergence of Ishikawa iterates of quasi-nonexpansive mappings
• Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings.
• Nonexpansive mappings and asymptotic regularity
• Iteration sequences for asymptotically quasi-nonexpansive mapping with an error member of uniform convex Banach space.
• On convergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings
• Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings
• Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
• Fixed Points by a New Iteration Method
• Iterative sequences for asymptotically quasi-nonexpansive mappings.
• Iterative sequences for asymptotically quasi-nonexpansive mappings with error member

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