<p>Recent advances using inertial acceleration strategies for monotone operators have yet to be fully explored within the context of accretive operators. It is well-known that the class of accretive operators is closely connected to the important class of pseudocontractive operators. This paper proposes a viscosity-type algorithm with double inertial steps for finding a common solution of inclusion problem and fixed point problem. The strong convergence theorem concerning the proposed algorithm is proved in the setting of real Banach spaces. Furthermore, applications of the theorem to convex minimization and image restoration problems are presented. In addition, the effect of the double step inertial acceleration strategy is studied by comparing the proposed method with its one-step and non-inertial counterpart in the literature using several numerical examples. Finally, the new method proves to be competitive and promising, outperforming many existing algorithms in all the considered examples.</p>