The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval

[摘要] As an important iteration, the Mann and Ishikawa iteration has extensive application in fixed point theory. In 1991, David Borwein and Jonathan Borwein proved the convergence of the Mann iteration on a closed bounded interval in their paper. In this paper, we will extend their result to an arbitrary interval and to the Ishikawa iteration, indicating the necessary and sufficient condition for the convergence of Ishikawa iteration of continuous functions on an arbitrary interval. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-11-15

[关键词] arbitrary interval;real function;fixed point;Ishikawa iteration