| h-凸函数 |
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| 引用本文： | 焦合华. h-凸函数[J]. 昆明理工大学学报(自然科学版), 2007, 32(4): 114-119 |
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| 作者姓名： | 焦合华 |
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| 作者单位： | 长江师范学院,数学系,重庆,涪陵,408003 |
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| 摘 要： | 针对凸函数,s-凸函数,Godunova-Levin函数和P-函数定义的特点,引入了一类新的广义凸函数——h-凸函数,它推广了凸函数、s-凸函数、Godunova—Levin函数和P-函数的概念;接着,讨论了h-凸函数的一些有用性质;最后,利用h函数的上(下)积性给出了h-凸函数在不等式中的2个应用,推广了Schur和Jensen不等式.
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| 关 键 词： | 凸函数 积性函数 Schur不等式 Jensen不等式 |
| 文章编号： | 1007-855X（2007）04-0114-06 |
| 修稿时间： | 2007-03-04 |
h - Convex Functions |
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| JIAO He-hua. h - Convex Functions[J]. Journal of Kunming University of Science and Technology(Natural Science Edition), 2007, 32(4): 114-119 |
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| Authors: | JIAO He-hua |
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| Affiliation: | Department of Mathematics, Yangtze Normal University, Fttling, Chongqing 408003, China |
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| Abstract: | Based on the characteristics of convex functions,s-convex function,Godunova-Levin function andP-function,a new class of generalized convex function ofh-convex is introduced,which generalizes the convex function,s-convex function,Godunova-Lcvin function and P-function: then,some important properties of h-convex function are discussed.Finally,by using super (sub) multiplicativity ofh-function two applications forh-convex function to inequalities are presented,which generalizes Schur and Jensen inequalities. |
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| Keywords: | convex function multiplicative function Schur sinequality Jensen's inequality |
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