engleski

On an Inequality Of H.G. Hardy

In this paper, we state, prove and discuss new general inequality for convex and increasing functions. As a special case of that general result we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann--Liouville type. Consequently, we get the inequality of H.G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as well as fractional integrals of a function with respect to another function. Finally we apply our main result to multidimensional settings to obtain new results involving mixed Riemann--Liouville fractional integrals.

The Riemann-Liouville fractional integrals ; convex function ; kernel

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