Some common-fixed-point results for nonself asymptotically quasi-nonexpansive mappings by a two-step iterative process (Q2923117)

Let \(K\) be a nonempty closed convex subset of a Banach space \(E\) and let \(P\) be a nonexpansive retraction of \(E\) onto \(K\). A non-self mapping \(T:K\to E\) is asymptotically quasi-nonexpansive with respect to \(P\) if the fixed-point set \(F(T):=\{x\in K:x=Tx\}\) is nonempty and there exists a sequence \(\{k_n\}\subset[1,\infty)\) such that \(\lim_nk_n=1\) and \(\|(PT)^nx-p\|\leq k_n\| x-p\|\) for all \(x\in K\) and for all \(n\geq 1\). The authors prove some convergence results of a two-step iterative process to a common fixed point of two asymptotically quasi-nonexpansive non-self mappings with respect to a common nonexpansive retraction.