Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

Hardy Type Inequalities via Convexity - the Journey so Far

It is nowadays well-known that Hardy’s inequality (like many other inequalities) follows directly from Jensen’s inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.

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...

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

On Hadamard-Type Inequalities Involving Several Kinds of Convexity

1 Department of Mathematics, K.K. Education Faculty, Atatürk University, Campus, 25240 Erzurum, Turkey 2 Research Group in Mathematical Inequalities & Applications, School of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia 3 School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, So...