Strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family of strictly nonself pseudocontractions
Summary: We deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by \(y_n = \beta_n S x_n + (1 - \beta_n)x_n, x_{n+1} = P_C[\alpha_n f(x_n) + (1 - \alpha_n) \sum^\infty_{i=1} \mu^{(n)}_i T_i y_n]\), and \(\forall n \geq 0\), where \(T_i : C \mapsto H\) is a nonself \(k_i\)-strictly pseudocontraction. Under certain approximate conditions, the sequence \(\{x_n\}\) converges strongly to \(x^\ast \in \bigcap^\infty_{i=1} F(T_i)\), which solves some variational inequality. The results here improve and extend some recent results.
scientific article; zbMATH DE number 6116405