Abstract
We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order $n\in N$ . Some new Hardy-type inequalities for this operator are proved and discussed.
Highlights
In FH Jackson defined q-derivative and definite q-integral [ ]
We introduce the q-analog of a polynomial in the following way: (x – a)nq :=
In what follows we investigate inequalities ( ) and ( )
Summary
In FH Jackson defined q-derivative and definite q-integral [ ] (see [ ]). It was the starting point of q-analysis. The first results concerning integral inequalities in q-analysis were proved in by Gauchman [ ]. ) concerning discrete Hardy-type inequalities which are proved in [ ]. Inequality ( ) holds if and only if B(n) = max ≤m≤n– Bm(n) < ∞, where
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