{"title":"Extended power difference means","authors":"Shuhei Wada","doi":"10.1007/s44146-024-00137-7","DOIUrl":null,"url":null,"abstract":"<div><p>The extended power difference mean <span>\\(f_{a,b}(t):={b\\over a}{{t^a-1}\\over {t^b-1}}\\)</span> <span>\\((a,b\\in {\\mathbb {R}})\\)</span> is investigated in this paper. We show some Thompson metric inequalities involving <span>\\(f_{a,b}\\)</span> and Tsallis relative operator entropy. We also discuss the behavior of the bivariate function defined as the perspective map for <span>\\(f_{a,b}\\)</span>. Finally, the relationship beween <span>\\(f_{a,b}\\)</span> and the weighted logarithmic mean is studied.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"491 - 512"},"PeriodicalIF":0.5000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACTA SCIENTIARUM MATHEMATICARUM","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s44146-024-00137-7","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
The extended power difference mean \(f_{a,b}(t):={b\over a}{{t^a-1}\over {t^b-1}}\)\((a,b\in {\mathbb {R}})\) is investigated in this paper. We show some Thompson metric inequalities involving \(f_{a,b}\) and Tsallis relative operator entropy. We also discuss the behavior of the bivariate function defined as the perspective map for \(f_{a,b}\). Finally, the relationship beween \(f_{a,b}\) and the weighted logarithmic mean is studied.
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