Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems

Abstract

This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion (SpVIsP) and its extended version for estimating the common solution of (SpVIsP) and fixed point problem (FPP) of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example.