{"title":"A generalization and an application of the arithmetic-geometric mean inequality for the Frobenius norm.","authors":"Xuesha Wu","doi":"10.1186/s13660-018-1732-9","DOIUrl":null,"url":null,"abstract":"<p><p>Recently, Kittaneh and Manasrah (J. Math. Anal. Appl. 361:262-269, 2010) showed a refinement of the arithmetic-geometric mean inequality for the Frobenius norm. In this paper, we shall present a generalization of Kittaneh and Manasrah's result. Meanwhile, we will also give an application of Kittaneh and Manasrah's result. That is, we obtain an improvement of Jocić and Kittaneh's inequality which was presented in (Jocić and Kittaneh in J. Oper. Theory 31:3-10, 1994).</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1732-9","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1732-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/6/20 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
Recently, Kittaneh and Manasrah (J. Math. Anal. Appl. 361:262-269, 2010) showed a refinement of the arithmetic-geometric mean inequality for the Frobenius norm. In this paper, we shall present a generalization of Kittaneh and Manasrah's result. Meanwhile, we will also give an application of Kittaneh and Manasrah's result. That is, we obtain an improvement of Jocić and Kittaneh's inequality which was presented in (Jocić and Kittaneh in J. Oper. Theory 31:3-10, 1994).
最近，Kittaneh和Manasrah (J. Math。分析的应用361:262-269,2010)显示了Frobenius范数的算术-几何平均不等式的改进。在本文中，我们将对Kittaneh和Manasrah的结果进行推广。同时，我们也将对Kittaneh和Manasrah的结果进行应用。即对J. Oper中jociki and Kittaneh提出的jociki and Kittaneh不等式进行改进。理论31:3-10,1994)。
期刊介绍：
The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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