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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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