The convergence of the modified Mann iteration
is equivalent to the convergence of the modified Ishikawa iteration
where , when the map is asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive. Here for a Banach space and a nonempty subset of the map is called asymptotically nonexpansive in the intermediate sense (a.n.i.s.) if is continuous for some and
and is called strongly successively pseudocontractive (s.s.p.) if there exists and such that
for all and .