Diamond-? Hardy-Type Inequalities on Time Scales

Hardy–Leindler Type Inequalities on Time Scales

In this paper, we will prove some new dynamic inequalities on a time scale T. These inequalities, as special cases, when T= R contain some integral inequalities and when T= N contain the discrete inequalities due to Leindler. The main results will be proved by using the Hölder inequality and a simple consequence of Keller’s chain rule on time scales. From our results, as applications, we will d...

Hardy Type Inequalities on Time Scales

Time Scales Hardy–type Inequalities via Superquadracity

In this paper some new Hardy–type inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy–type inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and disc...

Diamond-alpha Integral Inequalities on Time Scales

The theory of the calculus of variations was recently extended to the more general time scales setting, both for delta and nabla integrals. The primary purpose of this paper is to further extend the theory on time scales, by establishing some basic diamond-alpha dynamic integral inequalities. We prove generalized versions of Hölder, Cauchy-Schwarz, Minkowski, and Jensen’s inequalities. For the ...

Some Opial-Type Inequalities on Time Scales

and Applied Analysis 3 where r t is positive and continuous function with ∫X a dt/r t < ∞, and if x b 0, then ∫b X |x t |∣∣x′ t ∣∣dt ≤ 1 2 ∫b