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Remarks of Equivalence among Picard, Mann, and Ishikawa Iterations in Normed Spaces
Fixed Point Theory and Applications volume 2007, Article number: 061434 (2007)
Abstract
We show that the convergence of Picard iteration is equivalent to the convergence of Mann iteration schemes for various Zamfirescu operators. Our result extends of Soltuz (2005).
References
Şoltuz ŞM: The equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators. Mathematical Communications 2005,10(1):81–88.
Vasilev FP: Numerical Methods for Solving Extremal Problems. 2nd edition. Nauka, Moscow, Russia; 1988:550.
Weng X: Fixed point iteration for local strictly pseudo-contractive mapping. Proceedings of the American Mathematical Society 1991,113(3):727–731. 10.1090/S0002-9939-1991-1086345-8
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Zhiqun, X. Remarks of Equivalence among Picard, Mann, and Ishikawa Iterations in Normed Spaces. Fixed Point Theory Appl 2007, 061434 (2007). https://doi.org/10.1155/2007/61434
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DOI: https://doi.org/10.1155/2007/61434