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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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Original Article

Kyungpook Mathematical Journal 2006; 46(2): 211-217

Published online June 23, 2006

Copyright © Kyungpook Mathematical Journal.

On the Equivalance of Some Fixed Point Iterations

Murat "{O}zdemir, Sezgin Akbulut

Atat"{u}tk "{U}niversitesi Fen-Edebiyat Fak"{u}ltesi Matematik B"{o}l"{u}m"{u}, 25240 Erzurum, Turkey

Abstract

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space.

Keywords: Mann Iteration, Ishikawa iteration, Noor iteration, Lipschitzian map