Strong Convergence Theorems for an Implicit Iterative Algorithm for the Split Common Fixed Point Problem

Abstract EN

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 xn=αnfxn+1-αnUλxn-ρnA*I-TAxn, n≥0, where Uλ=(1-λ)I+λU, 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.