| 向量值函数的导数 |
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| 引用本文： | 张月梅. 向量值函数的导数[J]. 松辽学刊, 2014, 0(1): 57-59,65 |
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| 作者姓名： | 张月梅 |
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| 作者单位： | [1]长江大学工程技术学院基础部,湖北荆州434020 [2]长江大学信息与数学学院,湖北荆州434020 |
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| 基金项目： | 湖北省教育科学＂十二五＂规划项目（2013B308） |
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| 摘 要： | 文章主要讨论了向量值函数的方向导数、Gateaux导数和Frechet导数的定义,并对它们之间的相互关系做了简单的讨论.证明了函数如果Frechet可微则一定Gateaux可微,如果Gateaux可微则一定方向可微;通过反例说明反之是不成立的,但增加一定的条件可使反过来也是成立的.最后还讨论了几个简单的性质.
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| 关 键 词： | 方向导数 Gateaux导数 Frechet导数 |
Differential of Vector Valued Functions |
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| ZHANG Yue-mei. Differential of Vector Valued Functions[J]. Songliao Journal (Natural Science Edition), 2014, 0(1): 57-59,65 |
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| Authors: | ZHANG Yue-mei |
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| Affiliation: | ZHANG Yue-mei ( 1. Yangtze University, School of Information and Mathematics, Jingzhou 434020, China; 2. Yangtze University College of Technology ＆ Engineering, Jingzhou 434020, China) |
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| Abstract: | The paper mainly discusses the directional differential, Gateaux differential and Frechet differential of vector valued functions, as well as the relationships between them. Proved that if a function is Frechet differenti- al, then it is Gateaux differential, if a function is Gateaux differential, then it is directional differential. Through the examples , we can see that the conclusions of opposite are not established, but increasing some conditions can make the opposite is also established. Finally, we also discussed several simple properties. |
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| Keywords: | directional differential Gateaux differential Frechet differential |
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