A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems

In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and $q$-uniformly smooth real Banach spaces ( q > 1 ). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space $l_4(\mathbb{R})$ to study the effect of the relaxation and inertial parameters in our proposed algorithm