Posts by Stefan Soltuz

Abstract

We show that the Mann and Ishikawa iterations are equivalently used to approximate fixed points of generalized contractions.

Authors

S.M. Soltuz
Tiberiu Popoviciu Institute of Numerical Analysis

B.E. Rhoades
Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA

Keywords

?

Paper coordinates

B.E. Rhoades, Ş.M. Şoltuz, The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions, Int. J. Math. Math. Sci. 2006 (2006), no. 6, 54653.

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About this paper

Journal

International Journal of Mathematics and Mathematical Sciences

Publisher Name

Wiley

DOI
Print ISSN

0161-1712

Online ISSN

1687-0425

google scholar link

[1] S. Ishikawa, Fixed points by a new iteration method, Proceedings of the American MathematicalSociety 44 (1974), no. 1, 147–150.
[2] W. R. Mann, Mean value methods in iteration, Proceedings of the American Mathematical Soci-ety 4 (1953), no. 3, 506–510.
[3] B. E. Rhoades, Convergence of an Ishikawa-type iteration scheme for a generalized contraction, Journal of Mathematical Analysis and Applications 185 (1994), no. 2, 350–355.
[4] B. E. Rhoades and S¸ . M. Soltuz, On the equivalence of Mann and Ishikawa iteration methods,International Journal of Mathematics and Mathematical Sciences 2003 (2003), no. 7, 451–459.
[5] , _____The equivalence between the convergences of Ishikawa and Mann iterations for an asymp-totically pseudocontractive map, Journal of Mathematical Analysis and Applications 283 (2003),no. 2, 681–688.
[6] ,______ The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators,International Journal of Mathematics and Mathematical Sciences 2003 (2003), no. 42, 2645–2651.
[7] , ______The equivalence between the convergences of Ishikawa and Mann iterations for an asymp-totically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps,Journal of Mathematical Analysis and Applications 289 (2004), no. 1, 266–278.
[8] , ______The equivalence of Mann iteration and Ishikawa iteration for a Lipschitzian ψ-uniformlypseudocontractive and ψ-uniformly accretive maps, Tamkang Journal of Mathematics 35 (2004),no. 3, 235–245.
[9] S. M. Soltuz, The equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contract-ive operators, Mathematical Communications 10 (2005), no. 1, 81–88.
[10] X. Weng, Fixed point iteration for local strictly pseudo-contractive mapping, Proceedings of the American Mathematical Society 113 (1991), no. 3, 727–731

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