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New iterative scheme for finite families of equilibrium, variational inequality, and fixed point problems in Banach spaces. (English) Zbl 1217.65105

Summary: We introduced a new iterative scheme for finding a common element in the set of common fixed points of a finite family of quasi-\(\varphi\)-nonexpansive mappings, the set of common solutions of a finite family of equilibrium problems, and the set of common solutions of a finite family of variational inequality problems in Banach spaces. The proof method for the main result is simplified under some new assumptions on the bifunctions.

MSC:

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