Carathéodory bounds for integer cones
✍ Scribed by Friedrich Eisenbrand; Gennady Shmonin
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 156 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0167-6377
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We prove the existence of a Carathéodory selection for a set-valued mapping satisfying standard conditions. Also, an application to random fixed point for random operators is established.
The purpose of the present paper is to derive some sufficient conditions for Carathéodory functions in the open unit disk by using Miller and Mocanu's lemma. Several special cases are considered as the corollaries of main results.
Several Filippov type implicit function theorems are known for Caratheodory Ž . Ž . Ž . functions f t, x , i.e., all f и, x are measurable and f t, и are continuous. We Ž . prove some generalisations of this theorem supposing only each function f t, и to be quasicontinuous with closed values.
We study a random Euler scheme for the approximation of Carathéodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte-Carlo method for integration proble