In this paper, we generalize some integral inequalities to more general situations. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of integral equations and differential equations. Applications are given to illustrate the usefulness of the inequalities.

The purpose of this paper is to investigate some nonlinear integral inequalities and their discrete analogues. The inequalities given here can be used as handy tools in the qualitative theory of certain differential equations, integral equations and difference equations. Mathematics subject classification (2010): 26D10, 26D15.

The theory of time scales was introduced by Hilger 1 in 1988 in order to contain both difference and differential calculus in a consistent way. Recently, many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales. For example, we refer the reader to the papers 2–12 and the references cited there in. In this paper, w...

Some new Iyengar type inequalities for an integral are obtained by using the generalised Taylor formula with integral remainder.

We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.

Some new Hilbert-Pachpatte discrete inequalities and their integral analogues are established in this paper. Other inequalities are also given in remarks.

In this paper we prove some new results concerning multi-dimensional Hardy type integral inequalities and also some corresponding limit Pólya–Knopp type inequalities.

Abstract In this paper, we study generalizations of some integral inequalities related to Hardy type via $(p, q)$ (p,q) -calculus. Many results obtained in paper provide extensions existing the literature. Furthermore, examples are given illust...