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A new iterative scheme for solving the equilibrium problems, variational inequality problems, and fixed point problems in Hilbert spaces. (English) Zbl 1244.65078

Summary: We introduce the new iterative methods for finding a common solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current literature.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47H10 Fixed-point theorems
49J40 Variational inequalities
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