Split feasibility and fixed-point problems for asymptotically quasi-nonexpansive mappings

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Publication Details

Author list: Deepho J., Kumam P.

Publisher: SpringerOpen

Publication year: 2013

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2013

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84887478296&doi=10.1186%2f1029-242X-2013-322&partnerID=40&md5=c9530e521a6ad24b8f8180763d4a67a6

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to introduce and analyze a weakly convergent theorem by using the regularized method and the relaxed extragradient method for finding a common element of the solution set Γ of the split feasibility problem and Fix(T) of fixed points of 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 assumptions. © 2013 Deepho and Kumam.

Keywords

Asymptotically quasi-nonexpansive mappings, Regularization, Relaxed extragradient methods