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Piri, Husain; Vaezi, Hamid

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

Fixed Point Theory Appl. 2010, Article ID 907275, 16 p. (2010).
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.

Cited in 1 Review
Cited in 10 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H20 Semigroups of nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

\(\delta \)-strongly accretive mapping; common fixed point; semigroup of non-expansive mappings; Hilbert space; strong convergence; variational inequality
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\textit{H. Piri} and \textit{H. Vaezi}, Fixed Point Theory Appl. 2010, Article ID 907275, 16 p. (2010; Zbl 1204.47083)
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