| 函数两种凸性定义等价性的今惑前世之初探 |
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| 引用本文： | 全然.函数两种凸性定义等价性的今惑前世之初探[J].大学数学,2021,37(1):72-76. |
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| 作者姓名： | 全然 |
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| 作者单位： | 河南工业大学 理学院,郑州 450001 |
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| 基金项目： | 高等学校大学数学教学研究;发展中心 2020 年教学改革项目;河南省高等教育教学改革研究项目;河南工业大学 2018 年本科教育教学改革研究;实践专项项目 |
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| 摘 要： | 通过研究中点凸函数和一般凸函数这两种凸性定义的早期发展历史和凸性性质来探索两种凸性定义的等价性.结果表明,两种凸性定义不等价;但是,当函数满足连续、可微、半连续和有界这四个条件中的任何一个条件时,两种凸性定义等价.
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| 关 键 词： | 两种凸性定义 连续 可微 半连续 有界 等价性 |
Some Researches on the Equivalence of the Two Definitions of Convex Function |
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| QUAN Ran.Some Researches on the Equivalence of the Two Definitions of Convex Function[J].College Mathematics,2021,37(1):72-76. |
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| Authors: | QUAN Ran |
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| Institution: | (College of Science,Henan University of Technology,Zhengzhou 450001, China) |
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| Abstract: | The equivalence of the two definitions of convex function is explored by the early history of the two definitions of the mid-convex function and the general convex function and by the properties of the two convex functions.The results imply that the two definitions of convexity are not equivalent.However,they are equivalent when the function satisfies any one of the four conditions:continuity,differentiability,semi-continuity and boundedness. |
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| Keywords: | two definitions of the convexity continuity differentiability semi-continuity boundedness equivalence |
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