{"title":"Some inequalities for convex functions and applications to operator inequalities","authors":"Duong Quoc Huy, Doan Thi Thuy Van","doi":"10.1142/s1793557123502169","DOIUrl":null,"url":null,"abstract":"In this paper we propose some Heinz-type inequalities for convex functions which provide a very simple proof of the main results of Kittaneh, Moslehian and Sababheh showed in the paper (F. Kittaneh, M. S. Moslehian and M. Sababheh, Quadratic interpolation of the Heinz means, Math. Inequal. Appl. 21(3) (2018) 739–757). We apply these inequalities to infer new inequalities for power means. As an application, we also give operator versions of Heinz-type inequalities for power and Heinz means.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian-European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793557123502169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we propose some Heinz-type inequalities for convex functions which provide a very simple proof of the main results of Kittaneh, Moslehian and Sababheh showed in the paper (F. Kittaneh, M. S. Moslehian and M. Sababheh, Quadratic interpolation of the Heinz means, Math. Inequal. Appl. 21(3) (2018) 739–757). We apply these inequalities to infer new inequalities for power means. As an application, we also give operator versions of Heinz-type inequalities for power and Heinz means.
本文提出了凸函数的一些Heinz型不等式，这些不等式非常简单地证明了Kittaneh, Moslehian和Sababheh在论文(F. Kittaneh, M. S. Moslehian和M. Sababheh, Heinz均值的二次插值，数学)中给出的主要结果。不平等的。苹果21(3)(2018)739-757)。我们应用这些不等式来推断新的幂均值不等式。作为应用，我们也给出了幂和均值的Heinz型不等式的算子版本。
期刊介绍：
Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.
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