Inertial iterative algorithms for common solution of variational inequality and system of variational inclusion problems

In this paper, we aim to consider a general variational inequality with a monotone operator and a system of nonlinear variational inclusion problems with two inverse strongly monotone operators and two maximal monotone operators in a real Hilbert space. A new algorithm for finding a common solution of the above problem is introduced. We describe how to incorporate the extragradient like method based on altering point technique with inertial effects and propose an iterative algorithm for finding the common solution of the above problem under consideration. A weak convergence theorem is obtained for the proposed algorithm. The results presented here are interesting and extend and improve the corresponding results Sahu and Singh (J Appl Math Comput 65: 351–378, 2020).