AN ITERATIVE METHOD WITH INERTIAL EFFECT FOR SOLVING MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM

Abstract

An iterative method with inertial extrapolation term for approximating the solution of multiplesets split feasibility problem in the infinite-dimensional Hilbert spaces is presented. In a recent paper, Ogbuisi and Mewomo [1] introduced an iterative algorithm involving an inertial term and a step size independent of the operator norm for approximating a solution to split variational inequality problem in a real Hilbert space. We extend the algorithm introduced by Ogbuisi and Mewomo [1] for solving multiple-set split feasibility problem, and we propose a self-adaptive technique to choose the stepsizes such that the implementation of our algorithm does not need prior information about the operator norm. We prove a weak convergence theorem to the proposed algorithm under some suitable conditions. Finally, we give some numerical examples to illustrate the efficiency and implementation of our method compared to some existing results.