On discrete inequalities for some classes of sequences

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-28 DOI:10.1515/math-2024-0021

Mohamed Jleli, Bessem Samet

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引用次数: 0

Abstract

For a given sequence

a = ( a 1 , … , a n ) ∈ R n

a=\left({a}_{1},\ldots ,{a}_{n})\in {{\mathbb{R}}}^{n}

, our aim is to obtain an estimate of

E n ≔ a 1 + a n 2 − 1 n ∑ i = 1 n a i

{E}_{n}:= \left|\hspace{-0.33em},\frac{{a}_{1}+{a}_{n}}{2}-\frac{1}{n}{\sum }_{i=1}^{n}{a}_{i},\hspace{-0.33em}\right|

. Several classes of sequences are studied. For each class, an estimate of

E n

{E}_{n}

is obtained. We also introduce the class of convex matrices, which is a discrete version of the class of convex functions on the coordinates. For this set of matrices, new discrete Hermite-Hadamard-type inequalities are proved. Our obtained results are extensions of known results from the continuous case to the discrete case.

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关于几类序列的离散不等式

对于给定序列 a = ( a 1 , ... , a n ) ∈ R n a=left({a}_{1},\ldots ,{a}_{n})\in {{{mathbb{R}}}^{n}, 我们的目的是获得 E n ≔ a 1 + a n 2 - 1 n ∑ i = 1 n a i {E}_{n}:=\left| {E}_{n}:=( a 1 , ... , a n ) 我们的目的是获得 E n ≔ a 1 + a n 2 - 1 n ∑ i = 1 n a i {E}_{n}:= \left|\hspace{-0.33em},\frac{{a}_{1}+{a}_{n}}{2}-\frac{1}{n}{\sum }_{i=1}^{n}{a}_{i},\hspace{-0.33em}\right| .本文研究了几类序列。对于每一类序列，我们都得到了 E n {E}_{n} 的估计值。我们还引入了凸矩阵类，它是坐标上凸函数类的离散版本。对于这组矩阵，我们证明了新的离散赫米特-哈达玛不等式。我们获得的结果是连续情况下已知结果在离散情况下的扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.