Generalization of Steffensen's inequality for higher order convex function involving extensions of montgomery identities on time scales

On generalized Hermite-Hadamard inequality for generalized convex function

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

A New Generalization of Ostrowski Type Inequality on Time Scales

(b− a)‖f ‖∞. (1) The inequality is sharp in the sense that the constant 14 cannot be replaced by a smaller one. For some extensions, generalizations and similar results, see [6, 9, 10, 11, 13, 14] and references therein. The development of the theory of time scales was initiated by Hilger [7] in 1988 as a theory capable to contain both difference and differential calculus in a consistent way. S...

Higher Order Dynamic Inequalities on Time Scales

In this paper, we will prove some new dynamic inequalities of higher orders on time scales. The results contain some continuous and discrete inequalities as special cases. We will prove the results by making use of Hölder’s inequality and Taylor monomials on time scales. Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40.

Lyapunov-type inequality for a higher order dynamic equation on time scales

The purpose of this work is to establish a Lyapunov-type inequality for the following dynamic equation [Formula: see text]on some time scale T under the anti-periodic boundary conditions [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text], [Formula: see text] with [Formula: see text] and [Formula: see text], p is the quotient of two odd positive intege...

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales