Strong Convergence Theorems for an Implicit Iterative Algorithm for the Split Common Fixed Point Problem. (14th December 2016) - He, Huimin; Liu, Sanyang; Chen, Rudong
Abstract : The aim of this paper is to construct a novel implicit iterative algorithm for the split common fixed point problem for the demicontractive operators U, T, and x n = α n f x n + 1 - α n U λ x n - ρ n A * I - T A x n, n ≥ 0, where U λ = ( 1 - λ ) I + λ U, and we obtain the sequence which strongly converges to a solution x ^ of this problem, and the solution x ^ satisfies the variational inequality. 〈 x ^ - f ( x ^ ), x ^ - z 〉 ≤ 0, ∀ z ∈ S, where S denotes the set of all solutions of the split common fixed point problem.