A Comparison of Mann and Ishikawa iterations of quasi-contraction operators

Olaleru, J.O (2007)

Staff publications

Article

It is generally conjectured that the Mann iteration converges faster than the Ishikawa iteration for any operator defined on an arbitrary closed convex subset of a Banach space. The recent result of Babu et al [1] shows that this conjecture can be proved for a class of quasi-contractive operators called the Zamfirescu operators[10]. In this paper it is shown that the proof can indeed be generalised to that of quasi-contraction maps.