Iterative Algorithm for Solving a Split Common Null Point Problem for Demicontractive Operators

Abstract

In this paper, first we introduce an iterative algorithm which does not require prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common null point problem of demicontractive mappings in a real Hilbert space. Widely known the computation of algorithms involving the operator norm for solving split common null point problem may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common null point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some numerical examples to illustrate our main result.