Some generalizations of the Hermite–Hadamard integral inequality

Some new generalizations of Hardy's integral inequality

We have studied some new generalizations of Hardy's integral inequality using the generalized Holder's inequality.

Some refinements and generalizations of Carleman's inequality

The constant is the best possible. There is a vast literature which deals with alternative proofs, various generalizations and extensions, and numerous variants and applications in analysis of inequality (1.1); see [1, 2, 3, 5, 7, 9, 8, 10, 13, 14, 15, 16, 17, 18, 19] and the references given therein. According to Hardy (see [6, Theorem 349]), Carleman’s inequality was generalized as follows. I...

On Bicheng-debnath’s Generalizations of Hardy’s Integral Inequality

We consider Hardy’s integral inequality and we obtain some new generalizations of Bicheng-Debnath’s recent results. We derive two distinguished classes of inequalities covering all admissible choices of parameter k from Hardy’s original relation. Moreover, we prove the constant factors involved in the right-hand sides of some particular inequalities from both classes to be the best possible, th...

On the Discrete Analogues of Some Generalizations of Gronwall's Inequality

1. We are concerned here with some discrete generalizations of the following result of GronwaU [1], which has been very useful in the study of ordinary differential equations: Lemma (Gronwall). I/ u(t) and v(t) are non-negative measurable ]unvtions /or t > 0 and Ct o is a non-negative constant, then the inequality t u(t) < uo + S v(s) u(s) ds (t > 0) (1.1) 0 implies that t u(t) < Uo exp (S v(s)...

A Duality in Integral Geometry; Some Generalizations of the Radon