Strong Convergence Theorems for an Implicit Iterative Algorithm for the Split Common Fixed Point Problem. (14th December 2016)

• Record Type: Journal Article
• Authors: He, Huimin; Liu, Sanyang; Chen, Rudong
• Other Names: Beg Ismat Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-12-14
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/4093524
• Languages: English
• ISSNs: 2314-8896

Abstract

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.