{"title":"扩展功率差意味着","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":"{\"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}","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}
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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