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A new iterative algorithm for the set of fixed-point problems of nonexpansive mappings and the set of equilibrium problem and variational inequality problem. (English) Zbl 1216.65066

Summary: We introduce a new iterative scheme and a new mapping generated by an infinite family of nonexpansive mappings and infinite real number. By using both of these ideas, we obtain a strong convergence theorem for finding a common element of the set of solutions of the equilibrium problem and the set of variational inequality and the set of fixed-point problems of the infinite family of nonexpansive mappings. Moreover, we apply our main result to obtain strong convergence theorems for finding a common element of the set of solutions of the equilibrium problem and the set of variational inequality and the set of common fixed points of pseudocontractive mappings.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
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References:

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