多重可变上限函数的半离散Hardy-Hilbert不等式

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (6): 167-172.

• 数理科学 • 上一篇

多重可变上限函数的半离散Hardy-Hilbert不等式

王爱珍^*, 杨必成

广东第二师范学院数学学院, 广东广州 510303

收稿日期:2023-11-10 发布日期:2025-12-31
通讯作者: 王爱珍(1975-),女,山东济南人,教授.Email:1320838229@qq.com
基金资助:
广东省教育科学规划课题(2022GXJK290),广东省重点建设学科科研能力提升项目(2022ZDJS109)

On a half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function

WANG Ai-zhen, YANG Bi-cheng

School of Mathematics, Guangdong University of Education, Guangzhou 510303, China

Received:2023-11-10 Published:2025-12-31

摘要/Abstract

摘要： 通过构造权系数,应用Hermite-Hadamard不等式与实分析的方法,得到一个新的更加精确的半离散Hardy-Hilbert不等式,此不等式涉及多重可变上限函数;作为应用,进一步探索并论证新不等式中最佳常数因子联系多参量的等价条件与一些取特殊参数值的不等式.

关键词: 权函数, Hermite-Hadamard不等式, 半离散Hardy-Hilbert不等式, 多重可变上限函数, 参量, 最佳常数因子

Abstract: By means of the weight functions, Hermite-Hadamard’s inequality, and the method of real analysis, a new and more accurate half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function is given. As applications, the equivalent conditions of the best possible constant factor related to a few parameters in the new inequality and some particular inequalities for taking special parameter values are further explored and demonstrated.

Key words: weight function, Hermite-Hadamard’s inequality, half-discrete Hardy-Hilbert’s inequality, multiple upper limit function, parameter, best possible constant factor

中图分类号:

O178

王爱珍, 杨必成. 多重可变上限函数的半离散Hardy-Hilbert不等式[J]. 兰州理工大学学报, 2025, 51(6): 167-172.

WANG Ai-zhen, YANG Bi-cheng. On a half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function[J]. Journal of Lanzhou University of Technology, 2025, 51(6): 167-172.

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多重可变上限函数的半离散Hardy-Hilbert不等式

On a half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function

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