کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1710342 | 1012885 | 2007 | 6 صفحه PDF | دانلود رایگان |

Let EE be an arbitrary Banach space and T:E→ET:E→E be a Lipschitzian and ϕϕ-hemicontractive mapping. This paper proves that, without the property liminfn→∞ϕ(t)/t>0liminfn→∞ϕ(t)/t>0, the Mann and Ishikawa iterative sequences with errors are weakly TT-stable. The related result deals with the weak TT-stability of these sequences with errors to the unique solution of the equation f=Txf=Tx when T:E→ET:E→E is Lipschitzian and ϕϕ-strongly accretive operator. Our results improve and generalize the recent results of Zhou et al. [H.Y. Zhou, S.S. Chang, Y.J. Cho, Weak stability of Ishikawa iteration procedures for ϕϕ-hemicontractive and accretive operators, Appl. Math. Lett. 14 (2001) 949–954] without the strict requirement liminfn→∞ϕ(t)/t>0liminfn→∞ϕ(t)/t>0 and extend the results to the Mann and Ishikawa iterations with errors.
Journal: Applied Mathematics Letters - Volume 20, Issue 4, April 2007, Pages 470–475