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On Jensen's gap by Taylor's theorem
Author(s) -
Agahi Hamzeh
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7514
Subject(s) - statistician , mathematics , jensen's inequality , calculus (dental) , mathematical economics , statistics , regular polygon , geometry , convex analysis , medicine , dentistry , convex optimization
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.