fink恒等式在高阶凸函数jensen型不等式中的应用

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI:10.2298/aadm230210018b

Marija Bosnjak, Mario Krnic, Josip Pecaric

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引用次数: 0

摘要

本文重点讨论了Fink恒等式在求解高阶凸函数jensen型不等式中的应用。除了基本形式外，我们还建立了与詹森不等式对应的超加性和单调性关系。我们也得到了相应的la - ribaric不等式。所得结果对偶凸度函数是有效的。利用这种方法，我们得到了幂均值之差的一些新的界，以及一些新的H?lder-type不平等

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Application of the fink identity to Jensen-type inequalities for higher order convex functions

The focus of this paper is the application of the Fink identity in obtaining Jensen-type inequalities for higher order convex functions. In addition to the basic form, we establish superadditivity and monotonicity relations that correspond to the Jensen inequality in this setting. We also obtain the corresponding Lah-Ribaric inequality. The obtained results are valid for functions of even degree of convexity. With this method, we derive some new bounds for the differences of power means, as well as some new H?lder-type inequalities

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).