AN ACCELERATED SHRINKING PROJECTION ALGORITHM FOR SOLVING THE SPLIT VARIATIONAL INCLUSION PROBLEM IN REFLEXIVE BANACH SPACES

The purpose of this article is to study the split variational inclusion problem in the framework of reflexive Banach spaces. In order to solve the problem, we propose a shrinking projection algorithm with inertial technique method and establish a strong convergence theorem. we also utilize our result to study the split variational inclusion problem in uniformly convex and uniformly smooth Banach spaces and the split convex minimization problem in reflexive Banach spaces. Finally, for supporting the convergence of the proposed algorithm, we also consider a numerical experiment.