The convergence of the modified Mann and Ishikawa iterations in Banach spaces

DOI10.1186/1029-242X-2013-188zbMath1364.47043WikidataQ59301542 ScholiaQ59301542MaRDI QIDQ394634

Guiwen Lv, Zhiqun Xue

Publication date: 27 January 2014

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

zbMATH Keywords

fixed pointreal Banach spaceasymptotically pseudocontractive mappinguniformly \(L\)-Lipschitz

Mathematics Subject Classification ID

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

Related Items (1)

New fixed point iteration and its rate of convergence

Cites Work

• On the strong convergence of the implicit iterative processes with errors for a finite family of asymptotically nonexpansive mappings
• Some results for uniformly \(L\)-Lipschitzian mappings in Banach spaces
• Stability of the Mann and Ishikawa iteration procedures for \(\phi\)-strong pseudocontractions and nonlinear equations of the \(\phi\)-strongly accretive type
• The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map.
• An example on the Mann iteration method for Lipschitz pseudocontractions
• A STRONG CONVERGENCE OF A MODIFIED KRASNOSELSKII‐MANN METHOD FOR NON‐EXPANSIVE MAPPINGS IN HILBERT SPACES
• Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings

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