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Approximation methods for common solutions of generalized equilibrium, systems of nonlinear variational inequalities and fixed point problems. (English) Zbl 1205.65185

Summary: We introduce an iterative method for finding a common element of the set of solutions of the generalized equilibrium problems, the set of solutions for the systems of nonlinear variational inequalities problems and the set of fixed points of nonexpansive mappings in Hilbert spaces. Furthermore, we apply our main result to the set of fixed points of an infinite family of strict pseudo-contraction mappings. The results obtained in this paper are viewed as a refinement and improvement of the previously known results.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J15 Abstract bifurcation theory involving nonlinear operators
47H10 Fixed-point theorems
47J20 Variational and other types of inequalities involving nonlinear operators (general)
65K15 Numerical methods for variational inequalities and related problems
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