## Strong convergence of a generalized iterative method for semigroups of nonexpansive mappings in Hilbert spaces.(English)Zbl 1204.47083

Summary: Using $$\delta$$-strongly accretive and $$\lambda$$-strictly pseudocontractive mapping, we introduce a general 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. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H20 Semigroups of nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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### References:

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