New Hardy-type integral inequalities

The proofs of generalized Hardy, Copson, Bennett, Leindler-type, and Levinson integral inequalities are revisited. It is contemplated to establish new proof of these classical inequalities using probability density function. New integral inequalities of Hardy-type involving the r th order Generalize...

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Bibliographic Details
Main Author: Manna Atanu
Format: Article
Published: 2020
Series:Acta scientiarum mathematicarum 86 No. 3-4
Kulcsszavak:Matematika, Integrálegyenlőtlenség
doi:10.14232/actasm-019-750-7

Online Access:http://acta.bibl.u-szeged.hu/73899
Description
Summary:The proofs of generalized Hardy, Copson, Bennett, Leindler-type, and Levinson integral inequalities are revisited. It is contemplated to establish new proof of these classical inequalities using probability density function. New integral inequalities of Hardy-type involving the r th order Generalized Riemann–Liouville, Generalized Weyl, Erdélyi–Kober, (k, ν)-Riemann–Liouville, and (k, ν)-Weyl fractional integrals are established through a probabilistic approach. The Kullback–Leibler inequality has been applied to compute the best possible constant factor associated with each of these inequalities.
Physical Description:467-491
ISSN:2064-8316