Inertial approximation method for split variational inclusion problem in Banach spaces

Abstract

In this paper, we introduce a new iterative algorithm of inertial form for approximating the solution of Split Variational Inclusion Problem (SVIP) involving accrective operators in Banach space. Motivated by the inertial technique, we incorporate the inertial term to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity of the SVIP associated mappings, we establish the weak convergence of the sequence generated by our algorithm. Some applications and numerical example are presented to illustrate the performance of our method as well as comparing it with the non-inertial version.