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Lv, Songtao

Strong convergence of a general iterative algorithm in Hilbert spaces. (English) Zbl 1278.47074

J. Inequal. Appl. 2013, Paper No. 19, 18 p. (2013).
Summary: In this paper, the problem of approximating a common element in the common fixed point set of an infinite family of nonexpansive mappings, in the solution set of a variational inequality involving an inverse-strongly monotone mapping, and in the solution set of an equilibrium problem, is investigated based on a general iterative algorithm. Strong convergence of the iterative algorithm is obtained in the framework of Hilbert spaces. The results obtained in this paper improve the corresponding results announced by many authors.

Cited in 5 Documents

MSC:

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

Keywords:

nonexpansive mapping; viscosity approximation method; equilibrium problem; fixed point; strong convergence
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References:

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