通过二次插值及其应用改进了jensen型不等式

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Mathematical Inequalities Pub Date : 2022-01-01 DOI:10.7153/jmi-2022-16-56

Duong Quoc Huy, T. Quang, Doan Thi Thuy Van

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引用次数: 0

摘要

．在论文中(J.数学)。不平等。11(2017)，第11号。(2)， Choi, Krni´c和Pe´cari´c利用线性插值改进了凸函数的jensen型不等式。他们的方法也为许多与Young-type和Heinz-type不等式相关的最新结果提供了一种单定的方法和更简单的证明。本文利用凸函数的二次插值，对由Choi、Krni′c和Pe′cari′c建立的jensen型不等式提出了新的修正。我们还给出了标量和算子情况下的young型和heinz型不等式的应用。

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Improved Jensen-type inequalities via quadratic interpolation and applications

. In the paper (J. Math. Inequal. 11 (2017), no. 2, 301–322.), Choi, Krni´c and Pe ˇ cari´c used the linear interpolation to improve Jensen-type inequalities for convex functions. Their method also provides a uni ﬁ ed approach with simpler proofs for many recent results related to Young-type and Heinz-type inequalities. In this paper, we propose new re ﬁ nements of Jensen-type inequalities established by Choi, Krni´c and Pe ˇ cari´c via the quadratic interpolation of convex functions. We also give Young-type and Heinz-type inequalities for both scalars and operator cases as an application.

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来源期刊

Journal of Mathematical Inequalities MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.90

自引率

3.40%

发文量

审稿时长

6-12 weeks

期刊介绍： The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts. ''JMI'' is published quarterly; in March, June, September, and December.