Iterative approximation of fixed points by using \(F\) iteration process in Banach spaces (Q1983351)

Summary: We connect the \(F\) iteration process with the class of generalized \(\alpha\)-nonexpansive mappings. Under some appropriate assumption, we establish some weak and strong convergence theorems in Banach spaces. To show the numerical efficiency of our established results, we provide a new example of generalized \(\alpha\)-nonexpansive mappings and show that its \(F\) iteration process is more efficient than many other iterative schemes. Our results are new and extend the corresponding known results of the current literature.