Convergence analysis of Picard–SP iteration process for generalized $$\alpha $$ –nonexpansive mappings

In this manuscript, we introduce a novel hybrid iteration process called the Picard–SP iteration process. We apply this new iteration process to approximate fixed points of generalized \(\alpha \)–nonexpansive mappings. Convergence analysis of our newly proposed iteration process is discussed in the setting of uniformly convex Banach spaces and results are correlated with some other existing iteration processes. The dominance of the newly proposed iteration process is exhibited with the help of a new numerical example. In the end, the comparison of polynomiographs generated by other well-known iteration processes with our proposed iteration process has been presented to make a strong impression of our proposed iteration process.