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

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  • Wei Xu
  • Yuanheng Wang

Abstract

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.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:457024
DOI: 10.1155/2012/457024
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