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Zbl 1203.47064
Plubtieng, S.; Thammathiwat, T.
(Plubtieng, Somyot; Thammathiwat, Tipphawan)
A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities. (English)
[J] J. Glob. Optim. 46, No. 3, 447-464 (2010). ISSN 0925-5001; ISSN 1573-2916/e

Summary: We introduce and study a new iterative scheme for finding the common element of the set of common fixed points of a sequence of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the general system of variational inequality for $\alpha $ and $\mu $-inverse-strongly monotone mappings. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main theorem extends a recent result of {\it L.-C.\thinspace Ceng, C.-Y.\thinspace Wang} and {\it J.-C.\thinspace Yao} [Math. Methods Oper. Res. 67, No.~3, 375--390 (2008; Zbl 1147.49007)] and many others.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
90C33 Complementarity problems

Citations: Zbl 1147.49007

Cited in: Zbl 1204.49006

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