On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application

In this article, we considered the class of generalized α,β-nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), generalized α-nonexpansive (GAN), and Reich–Suzuki nonexpansive (RSN) mappings. We used the iterative scheme JA for finding fixed points of these mappings in a Banach space setting. We provided both weak and strong convergence results under some mild conditions on the mapping, domain, and on the parameters involved in our iterative scheme. To support these results numerically, we constructed a new example of GABN mappings and proved that the JA iterative scheme converges to its fixed point. Moreover, we proved that JA iterative scheme converges faster to the fixed point corresponding to the some other iterative schemes of the literature. Eventually, we carried out an application of our main outcome to solve a split feasibility of problems (SFPs) in the setting of GABN mappings. Thus, our results were new in the literature and improved well-known results of the literature.