On the convergence of the multi-step Noor fixed point iterative scheme with errors in the class of Zamfirescu operators

MD. Asaduzzaman, M. Saleha Khatun, M. Zulfikar Ali

Abstract


The purpose of this paper is to establish a general theorem to approximate fixed points of Zamfirescu operators on an arbitrary normed space through the multi-step Noor fixed point iterative scheme with errors in the sense of Plubtieng and Wangkeeree [S. Plubtieng and R. Wangkeeree, Strong convergence theorem for multi-step Noor iterations with errors in Banach spaces, J. Math. Anal. Appl. 321 (2006), 10-23, 2006]. Our result generalizes and improves the corresponding results of Rafiq [A. Rafiq, A Convergence Theorem for Mann Fixed Point Iteration Procedure, Appl. Math. E-Notes, 6, 289-293], Xu [Y. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101], Liu [L. S. Liu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125], Osilike [ M. O. Osilike, Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type, J. Math. Anal. Appl. 213 (1997), 91-105] and several authors in literature.


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How to Cite this Article:

MD. Asaduzzaman, M. Saleha Khatun, M. Zulfikar Ali, On the convergence of the multi-step Noor fixed point iterative scheme with errors in the class of Zamfirescu operators, Advances in Fixed Point Theory, Vol 6, No 2 (2016), 150-166

Copyright © 2016 MD. Asaduzzaman, M. Saleha Khatun, M. Zulfikar Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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