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Some results on variational inequalities and generalized equilibrium problems with applications. (English) Zbl 1216.47099

The purpose of this paper is to introduce a general iterative method for finding a common element of the set of solutions of generalized equilibrium problems, the set of solutions of variational inequalities, and the set of common fixed points of a family of nonexpansive mappings in the framework of Hilbert spaces.
The results presented in this paper improve and extend many known results.

MSC:

47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
90C31 Sensitivity, stability, parametric optimization
47H05 Monotone operators and generalizations
47E05 General theory of ordinary differential operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
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