On the equivalence of the convergence criteria between modified Mann-Ishikawa and multi-step iterations with errors for successively strongly pseudo-contractive operators

DOI10.1016/J.AMC.2005.12.041zbMath1106.65050OpenAlexW2001834009MaRDI QIDQ849831

Fanwei Bu, Zhen Yu Huang, Muhammad Aslam Noor

Publication date: 31 October 2006

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

Full work available at URL: https://doi.org/10.1016/j.amc.2005.12.041

zbMATH Keywords

Mann-Ishikawa iterationmulti-step Noar iteration

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 (1)

Equivalency of convergence between one-step iteration algorithm and two-step iteration algorithm of variational inclusions for \(H\)-monotone mappings

Cites Work

• Iterative solution of nonlinear equations involving strongly accretive operators without the Lipschitz assumption
• The solution by iteration of nonlinear equations in uniformly smooth Banach spaces
• On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
• The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps.
• Iterative process with errors for fixed points of multivalued \(\Phi\)-hemicontractive operators in uniformly smooth Banach spaces
• New approximation schemes for general variational inequalities
• Approximating fixed points of \(\Phi\)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces
• Three-step iterations for nonlinear accretive operator equations
• The equivalence between Mann-Ishikawa iterations and multistep iteration
• Convergence theorems for multivalued \(\phi\)-hemicontractive operators and \(\phi\)-strongly accretive operators
• Some developments in general variational inequalities
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Nonlinear accretive and pseudo-contractive operator equations in Banach spaces
• Fixed Points by a New Iteration Method
• CONVERGENCE THEOREMS AND STABILITY PROBLEMS OF THE MODIFIED ISHIKAWA ITERATIVE SEQUENCES FOR STRICTLY SUCCESSIVELY HEMICONTRACTIVE MAPPINGS
• Mean Value Methods in Iteration

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