Some integral inequalities for approximately h—convex functions and their applications

Some Generalized Integral Inequalities and Their Applications

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.

New integral inequalities for $s$-preinvex functions

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.

On the generalization of some integral inequalities and their applications

On Some Advanced Integral Inequalities and Their Applications

In this paper, we obtain a generalization of advanced integral inequality and by means of examples we show the usefulness of our results.

On Some Integral Inequalities on Time Scales and Their Applications

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...