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Strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family of strictly nonself pseudocontractions. (English) Zbl 1253.65091
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.

##### MSC:
 65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx) 49J40 Variational inequalities 47H10 Fixed-point theorems
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