Two generalizations of the Gronwall inequality by product integration

Two Generalizations of Landau’s Inequality

Let π(x) be the number of prime numbers not exceeding x . In the introduction we present some inequalities related to this function; these have been presented in several articles about the Number Theory. In the present paper we obtain two inequalities which generalize Landau’s Inequality, π(2x) 2π(x) for any integer x 2 . Also, we obtain the inequality 2[xπ(x) + yπ(y)] > (x + y)π(x + y) , for a...

On Gronwall Inequality

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

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.

The Generalizations of Hilbert's Inequality

Generalizations of Hölder’s Inequality

Some generalized Hölder’s inequalities for positive as well as negative exponents are obtained. 2000 Mathematics Subject Classification. 26D07, 26D15.