A generalized f-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities

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Publication Details

Author list: Saewan S., Kumam P.

Publisher: Springer

Publication year: 2013

Volume number: 56

Issue number: 2

Start page: 623

End page: 645

Number of pages: 23

ISSN: 0925-5001

eISSN: 1573-2916

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84879019726&doi=10.1007%2fs10898-012-9922-3&partnerID=40&md5=2fe100a88c2a5226a954c2444d8333da

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to present new hybrid Ishikawa iteration process by the generalized f-projection operator for finding a common element of the fixed point set for two countable families of weak relatively nonexpansive mappings and the set of solutions of the system of generalized Ky Fan inequalities in a uniformly convex and uniformly smooth Banach space. Furthermore, we show that our new iterative scheme converges strongly to a common element of the afore mentioned sets. As applications, we apply our results to obtain some new results for finding a solution of a common fixed point of two countable in finite families, a system of generalized Ky Fan inequalities and a common zero-point problem for general B-monotone and maximal monotone operators in Banach spaces. The results presented in this paper improve and extend important recent results. ฉ 2012 Springer Science+Business Media, LLC.

Keywords

B-monotone mappings, Generalized f-projection operator, System of generalized Ky Fan inequalities, Weak relatively nonexpansive mapping