| 关于三阶可微函数的若干加权积分不等式 |
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| 引用本文： | 时统业,宋祥斌,陈根忠. 关于三阶可微函数的若干加权积分不等式[J]. 贵州师范大学学报(自然科学版), 2014, 0(2): 29-35 |
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| 作者姓名： | 时统业 宋祥斌 陈根忠 |
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| 作者单位： | 海军指挥学院浦口分院,江苏南京211800 |
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| 摘 要： | 通过建立与三阶可微函数有关的恒等式,在三阶导函数绝对值的幂为s-凸函数或s-凹函数的情形下,给出了若干新的加权Hermite-Hadamard型不等式。在三阶导函数有界的情形下,给出了一个严格的不等式。当权函数恒为1时,由本文的结果得到有关文献的结果。
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| 关 键 词： | 三阶可微函数 s-凸函数 s-凹函数 Hermite-Hadamard型不等式 |
Some weighted integral inequalities for differentiable functions |
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| SHI Tongye,SONG Xiangbin,CHEN Genzhong. Some weighted integral inequalities for differentiable functions[J]. Journal of Guizhou Normal University(Natural Sciences), 2014, 0(2): 29-35 |
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| Authors: | SHI Tongye SONG Xiangbin CHEN Genzhong |
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| Affiliation: | (Pukou Institute of Naval Command College, Nanjing, Jiangsu 211800, China) |
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| Abstract: | An identity in connection to three order differentiable functions is derived.Some new weighted Hermite-Hadamard type inequalities for three order differentiable functions whose third derivatives absolute value aroused to the qth power are s-convex and s-concave are established.A sharp inequality for three order differentiable functions whose third derivatives are bounded is obtained.When the weighted function is 1,the results in the existing literature can be derived from this paper. |
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| Keywords: | three order differentiable function s-convex function s-concave function Hermite-Hadamard type inequality |
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