Generalized Hölder’s and Minkowski’s inequalities for Jackson’s \(q\)-integral and some applications to the incomplete \(q\)-Gamma function. (English) Zbl 1470.26034

Summary: We establish some generalized Hölder’s and Minkowski’s inequalities for Jackson’s \(q\)-integral. As applications, we derive some inequalities involving the incomplete \(q\)-Gamma function.


26D15 Inequalities for sums, series and integrals
26E70 Real analysis on time scales or measure chains
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
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