Levinson和Ky Fan不等式的加权多数化及其改进

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-09-11 DOI:10.1016/j.bulsci.2025.103722

JinYan Miao

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引用次数: 0

摘要

本文有四个目标。首先，将积分多数化理论推广到若干不同权值的函数。在此基础上，我们改进了3-凸函数的Levinson不等式，从而对一些Ky Fan型不等式进行了统一和改进，对4-凸函数进行了稍微的探索，从而在高阶凸性的观点下进一步细化了Ky Fan不等式。文中还介绍了这种新型优化工具的其他一些应用。

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Weighted majorization and improvements for Levinson and Ky Fan inequalities

This article has four goals. First, integral majorization theory is largely generalized to several functions with different weights. Based on this tool, we improve Levinson inequality for 3-convex function, as consequences, some Ky Fan type inequalities can be unified and improved, 4-convex function can be slightly explored so that Ky Fan inequality is further refined under the view of higher-order convexity. Some more applications of the new majorization tool are also mentioned.

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