Mann's type extragradient for solving split feasibility and fixed point problems of Lipschitz asymptotically quasi-nonexpansive mappings

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Publication Details

Author list: Deepho J., Kumam P.

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-s2.0-84902580947&doi=10.1186%2f1687-1812-2013-349&partnerID=40&md5=a9bd6574ef8adc28e9645496f2f0a7b1

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to introduce and analyze Mann's type extragradient for finding a common solution set Γ of the split feasibility problem and the set Fix(T) of fixed points of Lipschitz asymptotically quasi-nonexpansive mappings T in the setting of infinite-dimensional Hilbert spaces. Consequently, we prove that the sequence generated by the proposed algorithm converges weakly to an element of Fix(T) ∩ Γ under mild assumption. The result presented in the paper also improves and extends some result of Xu (Inverse Probl. 26:105018, 2010; Inverse Probl. 22:2021-2034, 2006) and some others. ©2013 Deepho and Kumam; licensee Springer.

Keywords

Extragradient methods