Iterative sequences for asymptotically quasi-nonexpansive mappings with error member (Q5945746)

The paper concerns convergence of Ishikawa iterative sequences \((x_n)_n\) with error members for asymptotically quasi-nonexpansive mappings \(T:E\to E\). Here \(E\) is a nonempty closed convex set of a Banach space and the set \(F(T)\) of fixed points of \(T\) is nonempty. The main results state \((x_n)_n\) converges to a fixed point of \(T\) if and only if \(\liminf_{n\to\infty}d(x_n,F(T))=0\).