A modified inertial extragradient algorithm for some class of split variational inequality problem

A new inertial extragradient algorithm for approximating solutions of some class of split variational inequality problem in real Hilbert space is introduced and discussed. Furthermore, the sequence generated by our algorithm is shown to converge strongly to the solution of the aforementioned problem. Our result is obtained without the assumption of the Lipschitz constant of the underline operator, and also with minimal number of projections per iteration compare to other results on split variational inequality problems in the literature. A numerical example is presented to demonstrate and compare the versatility of our result. Our result extends and improves many recent results of this type in the literature.