A general composite explicit iterative scheme of fixed point solutions of variational inequalities for nonexpansive semigroups

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Publication Details

Author list: Kumam P., Wattanawitoon K.

Publisher: Elsevier

Publication year: 2011

Journal: Mathematical and Computer Modelling (0895-7177)

Volume number: 53

Issue number: #

Start page: 998

End page: 1006

Number of pages: 9

ISSN: 0895-7177

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-78751609518&doi=10.1016%2fj.mcm.2010.11.057&partnerID=40&md5=8ce2adfdca3e5872dda55dda530a693c

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we introduce a composite explicit viscosity iteration method of fixed point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces. We prove strong convergence theorems of the composite iterative schemes which solve some variational inequalities under some appropriate conditions. Our result extends and improves those announced by Li et al [General iterative methods for a one-parameter nonexpansive semigroup in Hilbert spaces, Nonlinear Anal. 70 (2009) 3065-3071], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, Fixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces, Math. Comput. Modelling 48 (2008) 279-286], Plubtieng and Wangkeeree [S. Plubtieng, R. Wangkeeree, A general viscosity approximation method of fixed point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces, Bull. Korean Math. Soc. 45 (4) (2008) 717-728] and many others. ฉ 2010 Elsevier Ltd.

Keywords

Viscosity iteration