Journal
MATHEMATICA SLOVACA
Volume 72, Issue 1, Pages 67-84Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/ms-2022-0005
Keywords
Inequalities; Hardy type inequalities; Green function; Taylor interpolating polynomial; Chebyshev functional; convex function; kernel; exponentially convex functions; log-convex functions; means
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In this paper, we use Taylor's formula to prove new Hardy-type inequalities involving convex functions. We introduce new results related to the Hardy-Hilbert inequality, Polya-Knopp inequality, and bounds for the identity related to the Hardy-type functional. Finally, we present mean value theorems of Cauchy type.
In this paper, we use Taylor's formula to prove new Hardy-type inequalities involving convex functions. We give new results that involve the Hardy-Hilbert inequality, Polya-Knopp inequality and bounds for the identity related to the Hardy-type functional. At the end, mean value theorems of Cauchy type are given.
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