## 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