A Cauchy–Khinchin integral inequality

A Version of Favard's Inequality for the Sugeno Integral

In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.

A Relation to Hardy-hilbert’s Integral Inequality and Mulholland’s Inequality

This paper deals with a relation between Hardy-Hilbert’s integral inequality and Mulholland’s integral inequality with a best constant factor, by using the Beta function and introducing a parameter λ. As applications, the reverse, the equivalent form and some particular results are considered.

On an Integral Inequality

In this article we give different sufficient conditions for inequality (∫ b a f(x)dx )β ≥ ∫ b a f(x)dx to hold.

A Hilbert Integral-Type Inequality with Parameters

A Reverse Hardy-hilbert-type Integral Inequality

By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.