Short proof of a discrete gronwall inequality

On Gronwall Inequality

In this paper, we obtained some new Gronwall-Bellman type integral inequalities and we give some consequences of our results.

A short proof of Paouris’ inequality

We give a short proof of a result of G. Paouris on the tail behaviour of the Euclidean norm |X| of an isotropic log-concave random vector X ∈ R, stating that for every t ≥ 1, P ` |X| ≥ ct √ n ́ ≤ exp(−t √ n). More precisely we show that for any log-concave random vector X and any p ≥ 1, (E|X|) ∼ E|X|+ sup z∈Sn−1 (E|〈z, X〉|). AMS Classification: 46B06, 46B09 (Primary), 52A23 (Secondary)

On an Inequality of Gronwall

In this paper, we obtain some new Gronwall-Bellman type integral inequalities, and we give an application of our results in the study of boundedness of the solutions of nonlinear integrodifferential equations.

A New Generalized Gronwall-Bellman Type Inequality

A SHORT PROOF OF A RESULT OF NAGEL

Let $(R,fm)$ be a Gorenstein local ring and$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are inthe same even liaison class, thenone has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.