The purpose of this research is to study existence and approximation of fixed points for generalized \(\alpha \) -nonexpansive (GAN) mappings on Banach spaces under an efficient computational fixed point method. We consider appropriate mild conditions on the mapping and domain and establish weak and strong convergence theorems. To support these theorems numerically, we construct a new example of GAN that exceeds the class of mappings with condition (C). We compare our numerical results with several iterative methods of the literature. Eventually, we solve a highly nonlinear problem in chemical reactor theory associated with adiabatic tubular reactors. The presented work is new in the literature and improves several corresponding results.
