An inertial-type extrapolation algorithm for solving the multiple-sets split pseudomonotone variational inequality problem in real hilbert spaces

This paper introduces and studies an inertial-type extrapolation algorithm for solving multiple-sets split variational inequality problem in the framework of real Hilbert spaces when the underlying finite families of operators are pseudomonotone. The method which involves inertial viscosity approximation uses self-adjustment stepsize condition that depends solely on the information of the previous step. Under certain suitable conditions on the algorithm parameters, we establish a strong convergence result of the proposed method without the prior knowledge of the operator norm or the coefficients of the underlying operators within the scope of real Hilbert spaces. As applications, some special forms of multiple-sets split variational inequality problems are given. The results present here extend and improve some already existing results in literature.