Weak convergence theorems for two nearly asymptotically nonexpansive non-self mappings

In this paper, we establish some weak convergence results of modified $S$-iteration process to converge to common fixed points involving two nearly asymptotically nonexpansive non-self mappings in the framework of uniformly convex Banach space under the following conditions (i) the Banach space $E$ satisfying Opial condition and (ii) the dual $E^{\ast}$ of $E$ has the Kadec-Klee property. Our results extend and improve many known results from the existing literature.