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Open Access Research

Data dependence results of new multi-step and S-iterative schemes for contractive-like operators

Faik Gürsoy1, Vatan Karakaya2* and Billy E Rhoades3

Author Affiliations

1 Department of Mathematics, Faculty of Science and Letters, Yildiz Technical University, Davutpasa Campus, Esenler, Istanbul, 34220, Turkey

2 Department of Mathematical Engineering, Faculty of Chemical and Metallurgical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, Istanbul, 34210, Turkey

3 Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA

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Fixed Point Theory and Applications 2013, 2013:76  doi:10.1186/1687-1812-2013-76

Published: 28 March 2013

Abstract

In this paper, we prove that the convergence of a new iteration and S-iteration can be used to approximate the fixed points of contractive-like operators. We also prove some data dependence results for these new iteration and S-iteration schemes for contractive-like operators. Our results extend and improve some known results in the literature.

MSC: 47H10.

Keywords:
new multi-step iteration; S-iteration; data dependence; contractive-like operator