| 关于Banach空间中凸泛函的广义次梯度不等式 |
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| 引用本文： | 姚云飞,徐森林.关于Banach空间中凸泛函的广义次梯度不等式[J].应用数学,2003,16(3):136-140. |
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| 作者姓名： | 姚云飞 徐森林 |
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| 作者单位： | 1. 阜阳师范学院数学系,安徽阜阳,236032
2. 中国科学技术大学数学系,安徽,合肥,230026 |
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| 摘 要： | 本文在前人^1,2]的基础之上，以凸泛函的次梯度不等式为工具，将Jensen不等式推广到Banach空间中的凸泛函，导出了Banach空间中的Bochner积分型的广义Jensen不等式，给出其在Banach空间概率论中某些应用，从而推广了文献3—6]的工作．
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| 关 键 词： | Banach空间 凸泛函 广义次梯度不等式 Jensen不等式 Bochner积分型 概率论 Gateaux可微 期望 σ代数 下鞅 |
| 文章编号： | 1001-9847(2003)03-0136-05 |
| 修稿时间： | 2002年10月21 |
On the Subgradient Inequality of Convex Functionals in Banach Spaces |
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| YAO Yun fei ,XU Sen lin.On the Subgradient Inequality of Convex Functionals in Banach Spaces[J].Mathematica Applicata,2003,16(3):136-140. |
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| Authors: | YAO Yun fei XU Sen lin |
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| Institution: | YAO Yun fei 1,XU Sen lin 2 |
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| Abstract: | In recent years the theory of convex functionals has been developing very fast.Many results of linear functionals are generalized in convex functionals,based on 1]and 2]in the light of thinking of generlization.In this paper,this paper gives on the subgradient inequality of convex functionals in the Banach spaces and its stochastie analysis applications of convex functionals and their applications,by means of subgraduent inequality of convex functionals thus generalizing the result of 3],4],5],6]. |
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| Keywords: | Convex functionals Subgradient inequality Banach space Gateaux defferenliable Bochner integrable Measure space Closed linear openator |
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