Umut Mutlu Özkan

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.

Fractional Quantum Integral Inequalities

The aim of the present paper is to establish some fractional -integral inequalities on the specific time scale, , a nonnegative integer, where , and .

Grüss type inequalities for double integrals on time scales

We prove some Gruss type inequalities for double integrals on time scales and unify the corresponding continuous and discrete versions from the literature. We also apply our results to the quantum calculus case.

Steffensen's Integral Inequality on Time Scales

We establish generalizations of Steffensens integral inequality on time scales via the diamond- dynamic integral, which is defined as a linear combination of the delta and nabla integrals.

Oscillations of dynamic equations on time scales with advanced arguments

In this paper, we investigated the oscillatory behaviour of solutions of advanced dynamic equations on time scales. Under the assumption that the τ is non-monotone or nondecreasing, we present new sufficient conditions for the oscillation of first-order delay dynamic equations on time scales. An example illustrating the result is also given.

On the Hilbert Type Integral Inequalities with Some Parameters and Its Reverse

This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.