Abstract
In this paper, we introduce a new and more general class of mappings that extends the Suzuki-type nonexpansive mapping. We first establish the existence of fixed points for this new class of mappings. Then, we propose an iterative scheme to approximate the fixed point and prove its convergence, rate of convergence, and data dependence results. A numerical example is presented to demonstrate the effectiveness of the proposed iterative scheme. Finally, we apply our results to solve boundary value problems, illustrating the practical usefulness of the proposed approach.