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Zbl 1093.47058
Iiduka, Hideaki; Takahashi, Wataru
Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings. (English)
[J] Nonlinear Anal., Theory Methods Appl. 61, No. 3, A, 341-350 (2005). ISSN 0362-546X

The authors suggest and analyze an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequalities involving a strongly monotone (inverse-strongly monotone) mapping in a Hilbert space under some conditions. Some applications are also indicated. The paper is well written and contains some nice results.
[Muhammad Aslam Noor (Islamabad)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H05 Monotone operators (with respect to duality)
49J40 Variational methods including variational inequalities
47H09 Mappings defined by "shrinking" properties
47J20 Inequalities involving nonlinear operators

Keywords: metric projection; inverse-strongly monotone mapping; nonexpansive mappings; fixed points; variational inequalities; iterative schemes; strong convergence

Cited in: Zbl 1187.47049 Zbl 1204.47084 Zbl 1196.47047 Zbl 1170.47044 Zbl 1170.47047 Zbl 1170.47046 Zbl 1153.49011

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