Sufficient conditions for Carathéodory functions
✍ Scribed by In Hwa Kim; Nak Eun Cho
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 403 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
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.
📜 SIMILAR VOLUMES
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 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.