Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions

This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by yn=βnSxn+(1-βn)xn, xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and ∀n≥0, where Ti:C↦H is a nonself ki-strictly pseudocontraction. Under certain ap...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2012-01, Vol.2012 (2012), p.607-617-341
Main Authors: Xu, Wei, Wang, Yuanheng
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convergence
Hilbert space
Inequalities
Inequality
Iterative algorithms
Iterative methods
Methods
Optimization
Studies
Titanium
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Summary:This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by yn=βnSxn+(1-βn)xn, xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and ∀n≥0, where Ti:C↦H is a nonself ki-strictly pseudocontraction. Under certain approximate conditions, the sequence {xn} converges strongly to x*∈⋂i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/457024