A Strengthened Form of a General Hardy-Type Inequality Obtained via Superquadraticity and Its Applications

Abstract

In this paper, we establish a new refined version of the general Hardy-type inequality utilizing the notion of superquadratic functions. The general result obtained is then applied to some particular one-dimensional and multidimensional settings providing generalizations and refinements of some well-known Hardy-type inequalities. Finally, as another consequence of the main result, we also state and prove a class of improved versions of some HardyHilbert-type inequalities.

Extension of Hardy-Type Inequalities on Time Scales

“…Proof. combining (2.4), Corollary 2.6 if the power is raised to s and Minkowski integral inequality [25]. We obtain the following inequality (4.2)…”