On Jensen'S Gap By Taylor'S Theorem
MATHEMATICAL METHODS IN THE APPLIED SCIENCES（2021）
摘要
An important tool in probability and mathematics is Jensen's gap. Sharper bounds for the Jensen gap were studied by many researchers. In this paper, we first introduce Jensen-Petrov's inequalities which improve the results of Liao and Berg on Jensen's gap (Liao, J. G., Berg, A. [2019]. The American Statistician 73: 278-281). We also present a modified version of Jensen-Petrov's inequality.
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关键词
convex function, Jensen-Petrov's inequality, Jensen's inequality, Taylor's theorem
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