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On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems. (English) Zbl 1310.47095

Summary: Our aim is introduce a new class of procedures, the Uniformly Asymptotically Regular-class of procedures (UAR-precedures). Then by a UAR-procedure we prove the convergence of two explicit iterative methods to the unique solution of a variational inequality problem on the set of common fixed points of a family of mappings, in the setting of Hilbert spaces.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
49J40 Variational inequalities
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