The modified Mann type iterative algorithm for a countable family of totally quasi-φ-asymptotically nonexpansive mappings by the hybrid generalized f-projection method

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Author list: Saewan S., Kanjanasamranwong P., Kumam P., Cho Y.J.

Publisher: SpringerOpen

Publication year: 2013

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2013

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84877059145&doi=10.1186%2f1687-1812-2013-63&partnerID=40&md5=7d3ee52a99ea8a2202e45d99a6ae3bd1

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this article is to introduce the modified Mann type iterative sequence, using a new technique, by the hybrid generalized f-projection operator for a countable family of totally quasi-φ- asymptotically nonexpansive mappings in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Then we prove that the modified Mann type iterative scheme converges strongly to a common element of the sets of fixed points of the given mappings. Our result extends and improves the results of Li et al. (Comput. Math. Appl. 60:1322-1331, 2010), Takahashi et al. (J. Math. Anal. Appl. 341:276-286, 2008) and many other authors. MSC: 47H05, 47H09, 47H10. © 2013 Saewan et al.; licensee Springer.

Keywords

Generalized f-projection operator, modified Mann type iterative sequence, Totally quasi-φ-asymptotically nonexpansive mapping