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 l4(R) to study the effect of the relaxation and inertial parameters in our proposed algorithm.