Inertial split projection and contraction method for pseudomonotone variational inequality problem in Banach spaces

In this article, we introduce a Halpern iterative method together with an inertial projection and contraction method for finding an approximate solution of variational inequality problem involving pseudomonotone mapping which also solves split common fixed point problem of Bregman demigeneralized mapping and Bregman strongly nonexpansive mapping in the framework of -uniformly convex and uniformly smooth real Banach spaces. Using our iterative method, we establish a strong convergence result for approximating the solution of the aforementioned problems and state some consequences of our main result. The result discussed in this article extends and complements many related results in the literature.