A general composite explicit iterative scheme of fixed point solutions of variational inequalities for nonexpansive semigroups. (English) Zbl 1218.47105

Summary: We introduce a composite explicit viscosity iteration method for 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 appropriate conditions. Our results extend and improve those announced by S.-H. Li, L.-H. Li and Y.-F. Su [Nonlinear Anal., Theory Methods Appl. 70, No. 9, A, 3065–3071 (2009; Zbl 1177.47075)], S. Plubtieng and R. Punpaeng [Math. Comput. Modelling 48, No. 1–2, 279–286 (2008; Zbl 1145.47308)], S. Plubtieng and R. Wangkeeree [Bull. Korean Math. Soc. 45, No. 4, 717–728 (2008; Zbl 1169.47055)], and many others.


47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
65K15 Numerical methods for variational inequalities and related problems
47H20 Semigroups of nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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