@Article{JCM-17-5,
author = {Zhao, Shuang-Suo and Wang, Chang-Yin and Zhang, Guo-Feng},
title = {Relations Between Two Sets of Functions Defined by the Two Interrelated One-Side Lipschitz Conditions},
journal = {Journal of Computational Mathematics},
year = {1999},
volume = {17},
number = {5},
pages = {457--462},
abstract = {<p style="text-align: justify;">In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the right-hand function $f(y)$ satisfy one-side Lipschitz condition $$ &lt;f(y)-f(z),y-z&gt; ≤&nbsp;v&#39; ||y-z||^2,f: \Omega \subseteq C^m&nbsp;→&nbsp;C^m,$$ or another related one-side Lipschitz condition $$[F(Y)-F(Z),Y-Z]_D ≤ v&#39;&#39; ||Y-Z||^2_D, F:\Omega^s \subseteq&nbsp;C^{ms} → C^{ms},$$ this paper demonstrates that the difference of the two sets of all functions satisfying the above two conditions respectively is at most that $v&#39;-v&#39;&#39;$ only is constant independent of stiffness of function $f$.&nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/1999-JCM-9117},
url = {https://global-sci.com/article/85643/relations-between-two-sets-of-functions-defined-by-the-two-interrelated-one-side-lipschitz-conditions}
}