Inertial Halpern-type Tseng’s method for approximating a solution to monotone inclusion problems with fixed point constraint

In this paper, we introduce an iterative method for approximating the common solution of a finite family of monotone inclusion problems and fixed point problem of a finite family of relatively nonexpansive mappings in reflexive Banach spaces. Our proposed method contains the inertial technique and the Halpern method. We obtain a strong convergence result without the prior knowledge of the Lipschitz constants of the mappings. Finally, we present some numerical experiments to demonstrate the applicability of our method. Several existing results in the literature are improved, extended, and generalized by our result.