An integral inequality with applications

An Integral Inequality and Its Applications

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 More Generalized Gronwall-like Integral Inequality with Applications

This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations. 1. Introduction. It is well known that integral inequalities play a very crucial role in the stud...

An Opial-type inequality with an integral boundary condition

We determine the best constant K and extremals of the Opial-type inequality ∫ b a |yy ′| dx ≤ K(b − a) ∫ b a |y ′|2 dx where y is required to satisfy the boundary condition ∫ b a y dx = 0. The techniques employed differ from either those used recently by Denzler to solve this problem or originally to prove the classical inequality; but they also yield a new proof of that inequality.

On an Integral Inequality of Feng Qi

In this note, we study a general version of a problem posed by Feng Qi in [10] in the context of a measured space endowed with a positive finite measure. For other studies and results, one can consult the papers [2], [3], [5], [8], [9], [12], [13] and [14]. Our basic tool is the classical Hölder inequality. By the convexity method (see [3]) we give an interpretation of the lower bound occuring ...