A Modified inertial Halpern method for solving split monotone variational inclusion problems in Banach Spaces

In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solutions of split monotone variational inclusion problems which is also a fixed point problem of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Moreover, our iterative method uses stepsize which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We apply our result to solve split feasibility problems and display some numerical examples to show the performance of our result with the existing ones. The result present in this article unifies and extends several existing results in literature.