Improved discrete inequalities in n independent variables

Concentration inequalities for functions of independent variables

Following the entropy method this paper presents general concentration inequalities, which can be applied to combinatorial optimization and empirical processes. The inequalities give improved concentration results for optimal travelling salesmen tours, Steiner trees and the eigenvalues of random symmetric matrices. 1 Introduction Since its appearance in 1995 Talagrand’s convex distance inequali...

ON SOME NEW RETARD INTEGRAL INEQUALITIES IN n INDEPENDENT VARIABLES AND THEIR APPLICATIONS

In this paper, we established some retard integral inequalities in n independent variables and by means of examples we show the usefulness of our results.

Nonlinear Integral Inequalities in Two Independent Variables on Time Scales

Some Nonlinear Integral Inequalities in Two Independent Variables

It is well known that the integral inequalities involving functions of one and more than one independent variables which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of differential equations. In the past few years, a number of integral inequalities had been established by many scholars, which are motivated by certain applications. For de...

New half-discrete Hilbert inequalities for three variables

In this paper, we obtain two new half-discrete Hilbert inequalities for three variables. The obtained inequalities are with the best constant factor. Moreover, we give their equivalent forms.