Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions

Abstract

In this paper we extend general Hardy’s inequality by appropriately combining Montgomery’s identity and Green functions. Related Grüss and Ostrowski-type inequalities are also derived.

Generalizations of Hardy Type Inequalities by Abel–Gontscharoff’s Interpolating Polynomial

“…φ( f (y))v(y)dµ 2 (y) (4) holds for all measurable functions f : Ω 2 → R, such that Im f ⊆ I, where A k is defined by (1) and (2).…”

The p-norm of circulant matrices

“…Let it therefore suffice to cite a few prominent contributions, such as the following monographs [2,5,6,18,24].…”