Abstract
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 rth 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.
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Manna, A. New Hardy-type integral inequalities. ActaSci.Math. 86, 467–491 (2020). https://doi.org/10.14232/actasm-019-750-7
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DOI: https://doi.org/10.14232/actasm-019-750-7