Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively \(\Phi \)-pseudocontractive mappings without Lipschitzian assumptions

DOI10.1016/j.jmaa.2006.07.028zbMath1153.47307OpenAlexW2063089565MaRDI QIDQ1001250

Zhen Yu Huang

Publication date: 17 February 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.07.028

zbMATH Keywords

equivalence of convergencemodified Ishikawa iteration with errorsgeneralized strongly successively \(\Phi \)-pseudocontractive mappingsmodified mann iteration with errors

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Mann iteration of weak convergence theorems in Banach space ⋮ The equivalence of convergence results between Mann and multistep iterations with errors for uniformly continuous generalized weak \(\Phi\)-pseudocontractive mappings in Banach spaces ⋮ On the convergence of iterative processes for generalized strongly asymptotically \(\phi\)-pseudocontractive mappings in Banach spaces ⋮ On the convergence of Mann and Ishikawa iterative processes for asymptotically \(\phi\)-strongly pseudocontractive mappings ⋮ Exponential inequalities for Mann’s stochastic algorithm ⋮ Convergence theorem for fixed points of nearly uniformly \(L\)-Lipschitzian asymptotically generalized \(\Phi \)-hemicontractive mappings ⋮ The equivalence of convergence results between Ishikawa and Mann iterations with errors for uniformly continuous generalized \(\Phi\)-pseudocontractive mappings in normed linear spaces ⋮ A note on implicit and explicit Mann iterative processes for asymptotically \(\phi\)-strongly pseudocontractive mappings

Cites Work

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• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Iterative solution of nonlinear equations of the \(\Phi\)-strongly accretive type
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• Nonlinear semigroups and evolution equations
• An example on the Mann iteration method for Lipschitz pseudocontractions
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• Steepest descent approximations for accretive operator equations
• Nonlinear mappings of nonexpansive and accretive type in Banach spaces
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