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

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 $y_n={\beta }_{n}S{x}_n+(1-{\beta }_n)x_n$, $x_{n+1}=P_C[{\alpha }_{n}f(x_n)+(1-{\alpha }_n){\sum }_{i=1}^{\infty }{\mu }_i^{(n)}{T}_i{y}_n]$, and $\forall n\ge 0$, where $T_i:C\mapsto H$ is a nonself $k_i$-strictly pseudocontraction. Under certain approximate conditions, the sequence $\{x_n\}$ converges strongly to $x^{*}\in {\bigcap }_{i=1}^{\infty }F(T_i)$, which solves some variational inequality. The results here improve and extend some recent results.