{"title":"Sharp exponential type inequalities for the arc lemniscate sine function with applications","authors":"Jinl ng Niu, Miao-Kun Wang, Wei-Mao Qian, Yuming Chu, Hui-Zuo Xu","doi":"10.7153/jmi-2023-17-33","DOIUrl":null,"url":null,"abstract":". In this paper, by proving some monotonicity theorems of certain combinations of the arc lemniscate sine function and elementary functions, we obtain two classes of exponential type inequalities for the arc lemniscate sine function. As applications, sharp bounds for the lemniscatic mean in terms of the arithmetic, harmonic and geometric means are given, which extend some previously known results.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/jmi-2023-17-33","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
. In this paper, by proving some monotonicity theorems of certain combinations of the arc lemniscate sine function and elementary functions, we obtain two classes of exponential type inequalities for the arc lemniscate sine function. As applications, sharp bounds for the lemniscatic mean in terms of the arithmetic, harmonic and geometric means are given, which extend some previously known results.
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.
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