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
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