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Iterative methods for semigroups of nonexpansive mappings and variational inequalities. (English) Zbl 1217.47124

The authors introduce a hybrid iterative method for finding a common fixed point of a semigroup of nonexpansive mappings in a Hilbert space, with respect to a sequence of left regular means defined on an appropriate space of bounded real valued functions of the semigroup.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H20 Semigroups of nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
43A07 Means on groups, semigroups, etc.; amenable groups
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