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

—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 quasicontraction maps.

• Type: Conference
• Year: 2007
• Where: WCE
• Authors: Johnson O. Olaleru
• Keywords: Arbitrary Closed Convex, Ishikawa Iteration, Mann Iteration, WCE 2007, WCE 2008