| 弱条件Bellman不等式及其推广 |
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| 引用本文： | 宋建儒,肖筱南.弱条件Bellman不等式及其推广[J].西安石油大学学报(自然科学版),2003,18(1):71-72. |
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| 作者姓名： | 宋建儒 肖筱南 |
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| 作者单位： | 西安石油学院,信息科学系,陕西,西安,710065 |
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| 摘 要： | 讨论了弱条件下的两个 Bellman诱导不等式 ,证明了 Bellman不等式仍能在弱条件下成立 .在此基础上 ,进一步证明了非负不增趋于零的无穷序列 { ak}在相同弱化条件下 ,可将 Bellman不等式推广到更为广泛的形式 ∑∞k=1(- 1 ) k+ 1f (ak)≥ f(∑∞k=1(- 1 ) k+ 1ak) .这一数学结构的扩广 ,将对深入研究和分析变量之间的变化性状与相互制约 ,具有更加广泛的实用价值
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| 关 键 词： | Bellman不等式 弱条件 连续函数 无穷序列 交错级数 收敛 |
| 文章编号： | 1001-5361(2003)01-0071-02 |
| 修稿时间： | 2001年9月11日 |
Bellman Inequality and Its Generalization Under Weak Condition |
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| SONG Jian ru,XIAO Xiao nan.Bellman Inequality and Its Generalization Under Weak Condition[J].Journal of Xian Shiyou University,2003,18(1):71-72. |
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| Authors: | SONG Jian ru XIAO Xiao nan |
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| Abstract: | Two Bellman induced inequalities under weak condition are discussed. On the foundation of this, it is further proved that by means of nonnegative, decreasing and trending to zero infinite sequence {a k}, the Bellman inequality can be generalized to the wider form∑∞k=1(-1) k+1 f(a k)≥f(∑∞k=1(-1) k+1 a k) under the same weak condition. This mathematical structure will be of practical value to further studying and analyzing variance and interaction among variables. |
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| Keywords: | Bellman inequality weak condition continuous function infinite sequence alternate series convergence |
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