Journal
MATHEMATICAL AND COMPUTER MODELLING
Volume 53, Issue 5-6, Pages 998-1006Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2010.11.057
Keywords
Viscosity iteration; Variational inequality; Nonexpansive semigroup
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Funding
- Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand
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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. (C) 2010 Elsevier Ltd. All rights reserved.
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