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Zbl 1227.49013
Gu, Gendai; Wang, Shenghua; Cho, Yeol Je
Strong convergence algorithms for hierarchical fixed points problems and variational inequalities. (English)
[J] J. Appl. Math. 2011, Article ID 164978, 17 p. (2011). ISSN 1110-757X; ISSN 1687-0042/e

Summary: We introduce a new iterative scheme that converges strongly to a common fixed point of a countable family of nonexpansive mappings in a Hilbert space such that the common fixed-point is a solution of a hierarchical fixed-point problem. Our results extend the ones of Moudafi, Xu, Cianciaruso et al., and Yao et al.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
47J25 Methods for solving nonlinear operator equations (general)

Keywords: iterative scheme; nonexpansive mappings in a Hilbert space; hierarchical fixed- point problem

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