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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 =β n Sx n +(1-β n )x n ,x n+1 =P C [α n f(x n )+(1-α n ) i=1 μ i (n) T i y n ], and n0, where T i :CH is a nonself k i -strictly pseudocontraction. Under certain approximate conditions, the sequence {x n } converges strongly to x * i=1 F(T i ), which solves some variational inequality. The results here improve and extend some recent results.
65J15Equations with nonlinear operators (numerical methods)
49J40Variational methods including variational inequalities
47H10Fixed point theorems for nonlinear operators on topological linear spaces