Abstract:
In this paper, we present a further improvement of the reverse Hardy type inequality via $_{a^{+}}\mathfrak{I}_{\mu}^{\Phi}$ and $_{b^{-}}\mathfrak{I} _{\mu}^{\Phi}$, the proportional generalized fractional integral operators with respect to another strictly increasing continuous function $\mu$. We obtain a new result by using two parameters of integrability $p$ and $q$, some special cases are mentioned according to the choice of the function $\Phi$.
Keywords and phrases:$\mu$-proportional generalized fractional integral operators, Hardy inequality, Hölder inequality.
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