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| CHARACTERIZATION OF THE UPPER SUBDERIVATIVE AND ITS CONSEQUENCES IN NONSMOOTH ANALYSIS |
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Citation： |
Wang Yuntong.CHARACTERIZATION OF THE UPPER SUBDERIVATIVE AND ITS CONSEQUENCES IN NONSMOOTH ANALYSIS[J].Chinese Annals of Mathematics B,1991,12(4):480~494 |
| Page view： 922
Net amount： 849 |
Authors： |
Wang Yuntong; |
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| Abstract： |
It is proved that the upper subderivative of a lower semicontinuous function on Banaoh space is upper semicontinuous for the first variable as
$\[{x^'}{ \to _f}x,i.e.,{x^'} - x,f({x^'}) - f(x)\]$.
By taking account of the work of Treiman. it is further shown that the upper subderivative of a.1.s,o. function is the upper limit of the contingent directtional derivatives around the concorned point. This new characterization of the upper subberivative allows simple derivations and natural extension of many results, in nonsmooth analysis. |
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