| 具有上(下)导数的上(下)半连续函数单调性的一个充要条件 |
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| 引用本文： | 高民犀.具有上(下)导数的上(下)半连续函数单调性的一个充要条件[J].贵州师范大学学报(自然科学版),2004,22(3):90-91. |
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| 作者姓名： | 高民犀 |
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| 作者单位： | 贵阳医学院,数学教研室,贵州,贵阳,550004 |
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| 摘 要： | 据文 1]中将导数f′(x)≤ 0放宽到函数f(x)的连续且右导数f+ ′(x)≤ 0或f-′(x)≤ 0 (f+ ′(x)≥ 0 (或f-′(x)≥ 0 ) ,则f(x)为仍为非增 (降 )的。文中进一步将条件放宽到具有上 (下 )导数的上 (下 )半连续函数 ,仍得到满意的结果。
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| 关 键 词： | 上(下)半连续 上(下)导数 上(下)半连续函数 |
| 文章编号： | 1004-5570(2004)03-0090-02 |
| 修稿时间： | 2004年3月10日 |
A necessary and sufficient condition on monotonicity of upper(lower) semi-continuous function satisfied with upper(lower) derived function |
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| GAO Min-xi.A necessary and sufficient condition on monotonicity of upper(lower) semi-continuous function satisfied with upper(lower) derived function[J].Journal of Guizhou Normal University(Natural Sciences),2004,22(3):90-91. |
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| Authors: | GAO Min-xi |
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| Abstract: | The author in 1] has relaxed restrictions from f ′(x)≤0 to a continuous function and f_+′(x)≤0 or f_-′(x)≤0(f_+′(x)≥0 or f_-′(x)≥0). In this condition, the function is still a nonincreasing (nondecreasing) one. In this paper, the condition is relaxed to upper (lower) semi-continuous and upper (lower) derived function and the result is still satisfied. |
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| Keywords: | upper(lower) semi-continuous upper(lower) derived function upper(lower) semi-continuous function |
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