The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions

DOI10.1155/IJMMS/2006/54653zbMath1124.47048MaRDI QIDQ884240

Ştefan M. Şoltuz, Billy E. Rhoades

Publication date: 13 June 2007

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/53556

zbMATH Keywords

Banach spaceIshikawa iterationMann iterationgeneralized contractionapproximate fixed point

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Numerical solutions to equations with nonlinear operators (65J15)

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Cites Work

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• Convergence of an Ishikawa-type iteration scheme for a generalized contraction
• The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map.
• The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators
• The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps.
• On the equivalence of Mann and Ishikawa iteration methods
• Fixed Point Iteration for Local Strictly Pseudo-Contractive Mapping
• Fixed Points by a New Iteration Method
• Mean Value Methods in Iteration

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