{"title":"Monotonicity of weighted averages of convex functions","authors":"G. Jameson","doi":"10.7153/MIA-2020-23-33","DOIUrl":null,"url":null,"abstract":"We consider weighted averages of the form Bn(W, f ) = ∑r=0 wn,r f (r/n) , where W is a summability matrix and f is convex. Conditions are given for Bn(W, f ) to increase or decrease with n . It decreases whenever W is a Hausdorff mean. The sequence of Bernstein polynomials for a convex function is a special case. Mathematics subject classification (2010): 26D15, 40G05, 41A10.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"425-432"},"PeriodicalIF":0.9000,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Inequalities & Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/MIA-2020-23-33","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
We consider weighted averages of the form Bn(W, f ) = ∑r=0 wn,r f (r/n) , where W is a summability matrix and f is convex. Conditions are given for Bn(W, f ) to increase or decrease with n . It decreases whenever W is a Hausdorff mean. The sequence of Bernstein polynomials for a convex function is a special case. Mathematics subject classification (2010): 26D15, 40G05, 41A10.
期刊介绍：
''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.
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