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On the mean value theorem

 

作者: J.P. Penot,  

 

期刊: Optimization  （Taylor Available online 1988）
卷期: Volume 19, issue 2  

页码: 147-156

 

ISSN:0233-1934

 

年代: 1988

 

DOI:10.1080/02331938808843330

 

出版商: Akademic-Verlag

 

关键词: Contingent derivative;DINI derivative;drop;mean-value theorem;nonsmooth analysis;Primary:26 B 05;Secondary:49 A 27

 

数据来源: Taylor

 

摘要:

Mean value theorems for nonsmooth functions are presented. Two versions are given, both using the contingent derivative. In. the first one a tangential convexity condition is used. In the second one no convexity assumption is made but the estimate.involves the contingent derivativedf (x, b − a) offat points arbitrarily close to the segment [a, b]. The proof relies on the Bishop-Phelps-Daneš-Ekeland procedure.

 

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