Contractility of Iterative Operators in Ishikawa and Mann Methods
Yinghua Fu · Gongcheng shuxue xuebao · 2012
Let X be an arbitrary Banach space and T : X → X be a Lipschitz strongly accretive operator.It has been proven that for a given f ∈ E,the Ishikawa and the Mann iteration methods with errors converge strongly to the solution of the equation T x = f.This paper introduces some theorems and proves that the iterative operators T with some restrict in both iteration methods are actually contractive operators.At the same time,the convergence conditions for the Mann and the Ishikawa iteration methods as well as the estimates of their iteration errors are demonstrated naturally.The result shown in this paper extends many relevant conclusions recently obtained.