On the equivalence of Mann and Ishikawa iteration methods

DOI10.1155/S0161171203110198zbMath1014.47052MaRDI QIDQ1864286

Billy E. Rhoades, Ştefan M. Şoltuz

Publication date: 17 March 2003

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

Full work available at URL: https://eudml.org/doc/50099

zbMATH Keywords

Picard iterationsIshikawa iterationsMann iterations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10)

Related Items (12)

The equivalence between Mann-Ishikawa iterations and multistep iteration ⋮ Some results in fixed point theory and application to the convergence of some iterative processes ⋮ Simpler is also better in approximating fixed points ⋮ The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous \(\varphi \)-strongly accretive operators in uniformly smooth Banach spaces ⋮ The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions ⋮ The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map. ⋮ Implication between certain iterative processes via some enriched mappings ⋮ The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps. ⋮ On some convergence properties of the modified Ishikawa scheme for asymptotic demicontractive self-mappings with matricial parameterizing sequences ⋮ A reconsideration on equivalency of convergence between iterations for uniformly \(L\)-Lipschitzian operators ⋮ The equivalence between the \(T\)-stabilities of Mann and Ishikawa iterations ⋮ Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces

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