{"title":"Refined Berezin number inequalities via superquadratic and convex functions","authors":"Fengsheng Chien, M. Bakherad, M. Alomari","doi":"10.2298/fil2301265c","DOIUrl":null,"url":null,"abstract":"In this paper, we generalize and refine some Berezin number inequalities for Hilbert space operators. Namely, we refine the Hermite-Hadamard inequality and some other recent results by using the concept of superquadraticity and convexity. Then we extend these inequalities for the Berezin number. Among other inequalities, it is shown that if S, T ? L(H(?)) such that ber(T) ? ber(|S|) and f is a nonnegative superquadratic function, then f (ber (T)) ? ber(f (|S|)) ? ?ber (f (||S| ? ber (T)|)).","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/fil2301265c","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we generalize and refine some Berezin number inequalities for Hilbert space operators. Namely, we refine the Hermite-Hadamard inequality and some other recent results by using the concept of superquadraticity and convexity. Then we extend these inequalities for the Berezin number. Among other inequalities, it is shown that if S, T ? L(H(?)) such that ber(T) ? ber(|S|) and f is a nonnegative superquadratic function, then f (ber (T)) ? ber(f (|S|)) ? ?ber (f (||S| ? ber (T)|)).
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