Using a technique of monotonization, this paper investigates a generalized GronwallBellman type delay integral inequality with two independent variables on time scales. The result not only unifies some continuous inequalities and their discrete analogues but also extends some known integral inequalities on time scales. An application to the estimation of solutions of delay dynamic integral equa...

We give some further answers to the open problem posed in the article [Feng Qi, Several integral inequalities, J. Inequal. Pure and Appl. Math., 1(2) (2000), Art. 19. (http://jipam.vu.edu.au/article.php?sid=113]).] Being Qi’s inequality of moment type, we consider the moments of uniformly distributed random variables and construct certain suitable probability measures to solve the posed problem...

Let ρ and λ be Banach function norms with the Fatou property. Then the generalized Minkowski integral inequality ρ(λ(f x)) ≤ M λ(ρ(f y)) holds for all measurable functions f (x, y) and some fixed constant M if and only if there exists 1 ≤ p ≤ ∞ such that λ is p–concave and ρ is p–convex.

One extension of Hölder inequality in the frame of pseudo-analysis is given. The extension of Hölder inequality is presented for the case of g-semirings and some illustrative examples are given.

The classical Jensen inequality for concave function φ is adapted for the Sugeno integral using the notion of the subdifferential. Some examples in the framework of the Lebesgue measure to illustrate the results are presented.

where the constant factor π 1 is the best possible. This is the famous Hilbert’s integral inequality see 1, 2 . Owing to the importance of the Hilbert’s inequality and the Hilberttype inequality in analysis and applications, some mathematicians have been studying them. Recently, various improvements and extensions of 1.1 appear in a great deal of papers see 3–11 , etc. . Specially, Gao and Hsu ...

Integral Hamzeh Agahi,1,† Adel Mohammadpour,1,∗ Radko Mesiar,2,3,‡ S. Mansour Vaezpour1,§ Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368 Bratislava, Slovakia Institute of In...