In this paper, we introduce a novel iterative scheme that integrates the Mann iteration process with the implicit $\theta$-method to approximate fixed points of nonexpansive multivalued mappings in Banach spaces. Under suitable assumptions, we establish both weak and strong convergence results for the proposed algorithm. Furthermore, we demonstrate the applicability of our method to variational inclusion problems and convex optimization problems. A numerical example is presented to illustrate the efficiency and effectiveness of the approach.