Weak stability of Mann and Ishikawa iterations with errors for \(\phi\)-hemicontractive operators

DOI10.1016/j.aml.2006.06.006zbMath1175.47061OpenAlexW2004713599MaRDI QIDQ1001113

Zhen Yu Huang

Publication date: 12 February 2009

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2006.06.006

zbMATH Keywords

stabilityBanach spaceIshikawa iterationMann iteration\(\Phi\)-hemicontractive operatorfixed point iteration procedure

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (3)

Stability and convergence of a new composite implicit iterative sequence in Banach spaces ⋮ Necessary and sufficient condition for Mann iteration converges to a fixed point of Lipschitzian mappings ⋮ Implicit Mann fixed point iterations for pseudo-contractive mappings

Cites Work

• Unnamed Item
• Stability of the Mann and Ishikawa iteration procedures for \(\phi\)-strong pseudocontractions and nonlinear equations of the \(\phi\)-strongly accretive type
• Stable iteration procedures for nonlinear pseudocontractive and accretive operators in arbitrary Banach spaces
• Approximating fixed points of \(\Phi\)-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces
• Convergence theorems for multivalued \(\phi\)-hemicontractive operators and \(\phi\)-strongly accretive operators
• Iterative solution of nonlinear equations involving set-valued uniformly accretive operators.
• Weak stability of the Ishikawa iteration procedures for \(\phi\)-hemicontractions and accretive operators

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