Some new Hardy type inequalities with general kernels II

Abstract

Abstract. In this paper we prove new Hardy type inequalities with general kernels. We give new results that involve the Hardy-Hilbert and the Pólya-Knopp inequality. We also prove new results that involve n -convex functions.Mathematics subject classification (2010): 26D10, 26D15.

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

“…Hardy-type inequalities obtained by similar methods as in this paper were given in [15,[17][18][19][20]. We also draw attention to two papers [21,22] about Sherman's inequality and Montgomery identity.…”

“…If, additionally, φ is convex, then φ (s) ≥ 0 for s ∈ [α, β]. Furthermore, by assumption (19), the first factor under the integral on the right-hand side is also nonnegative. Therefore, the right-hand side of ( 20) is non-negative, so the left-hand side is as well, i.e., (18) holds.…”

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

“…Using the positivity and the linearity of functional A we can get corresponding mean-value theorems. We may also obtain new classes of exponentially convex functions and get new means of the Cauchy type applying the same method as given in [14][15][16][17][18][19][20][21]. Funding: This research received no external funding.…”