Hüseyin Yildirim

Extensions of certain integral inequalities on time scales

Abstract In this work, we establish Holder’s inequality, Minkowski’s inequality and Jensen’s inequality on time scales via the nabla integral and diamond- α dynamic integral, which is defined as a linear combination of the delta and nabla integrals.

The solutions of then-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution

AbstractIn this article, the operator

Some New Inequalities of Hermite-Hadamard`s Type

\diamondsuit _B^k

Steffensen's Integral Inequality on Time Scales

is introduced and named as the Bessel diamond operator iteratedk times and is defined by

THE HERMITE-HADAMARD'S INEQUALITY FOR SOME CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS AND RELATED RESULTS

\diamondsuit _B^k = [(B_{x_1 } + B_{x_2 } + \cdots + B_{x_p } )^2 - (B_{x_{p + 1} } + \cdots + B_{x_{p + q} } )^2 ]^k