More accurate dynamic Hardy-type inequalities obtained via superquadraticity

Utilizing the concept of a superquadratic function, in the present paper we establish some general weighted Hardy-type inequalities involving dynamic integral operators with a non-negative kernel. Our general results are then applied to some particular one-dimensional cases to provide refinements of some Hardy-type inequalities on time scales, known from the literature. In particular, we show that our results may be seen as generalizations of some recent results closely connected to classical one-dimensional Hardy’s, Pó lya-Knopp’s and Hardy-Hilbert’s inequalities on time scales.