Convergence of Multi-step Iterates with Errors for Uniformly Quasi-Lipschitzian Mappings

Singh Saluja, Gurucharan; Kumar Nashine, Hemant

doi:10.2478/v10324-012-0009-0

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Convergence of Multi-step Iterates with Errors for Uniformly Quasi-Lipschitzian Mappings

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 50 (2012): Issue 1 (November 2012)

By: Gurucharan Singh Saluja and Hemant Kumar Nashine

Open Access

|Nov 2012

Abstract

The aim of this paper is to give some necessary and sufficient conditions for multi-step iterative scheme with errors for a nite family of uniformly quasi-Lipschitzian mappings to converge to common fixed point in a real Banach space. Our results extend and improve the corresponding results of Quan [7], Liu [5, 6], Xu and Noor [9] and many others.

References

[1] M. K. Ghosh and L. Debnath, Convergence of Ishikawa iterates of quasi- nonexpansive mappings, J. Math. Anal. Appl., 207, (1997), 96-103.10.1006/jmaa.1997.5268
Search in Google Scholar
[2] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44, (1974), 147-150.10.1090/S0002-9939-1974-0336469-5
Search in Google Scholar
[3] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4, (1953), 506-510.10.1090/S0002-9939-1953-0054846-3
Search in Google Scholar
[4] W. V. Petryshyn and T. E. Williamson, Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl., 43, (1973), 459-497.10.1016/0022-247X(73)90087-5
Search in Google Scholar
[5] L. Qihou, Iterative sequences for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl., 259, (2001), 1-7.10.1006/jmaa.2000.6980
Search in Google Scholar
[6] L. Qihou, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, J. Math. Anal. Appl., 259, (2001), 18-24.10.1006/jmaa.2000.7353
Search in Google Scholar
[7] J. Quan, Three-step iterative sequences with errors for uniformly quasi-Lipschitzian mappings, Numer. Math. J. Chinese Univ. (English Ser.), 15, No.4, (November 2006), 306-311.
Search in Google Scholar
[8] K. K. Tan and H. K. Xu, Approximating _xed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178, (1993), 301-308.10.1006/jmaa.1993.1309
Search in Google Scholar
[9] B. L. Xu and M. A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 267, No.2, (2002), 444-453.10.1006/jmaa.2001.7649
Search in Google Scholar

DOI: https://doi.org/10.2478/v10324-012-0009-0 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 103 - 113

Published on: Nov 22, 2012

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

Uniformly quasi-Lipschitzian mapping,

multi-step iterative scheme with errors,

Related subjects:

© 2012 Gurucharan Singh Saluja, Hemant Kumar Nashine, published by West University of Timisoara
This work is licensed under the Creative Commons License.

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