Some results about Krasnosel'skiĭ-Mann iteration process

Volume 9, Issue 6, pp 4852--4859 http://dx.doi.org/10.22436/jnsa.009.06.120

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Authors

Hojjat Afshari - Faculty of Basic Science, University of Bonab, Bonab, Iran. Hassen Aydi - Department of Mathematics, College of Education of Jubail, University of Dammam, P. O. 12020, Industrial Jubail 31961, Saudi Arabia. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.

Abstract

We introduce a Mann type iteration method and give a result about strongly convergence of this iteration method to a fixed point of nonexpansive mappings on Banach spaces. Also, by using idea of Ishikawa iteration method, we introduce a new iteration method via two mappings on uniformly convex Banach spaces and we provide a result about strongly convergence of the iteration method to a common fixed points of the mappings.

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Keywords

• Fixed point
• Krasnosel'skiĭ-Mann iteration
• nonexpansive mapping.

MSC

•  47J25
•  47H09

References

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