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

Abstract EN

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.