Hadamard Product Versions of the Chebyshev and Kantorovich Inequalities (original) (raw)

Inequalities of Furuta and Mond–Pečarić on the Hadamard product

Journal of Inequalities and …, 2000

As a continuation of (J. Mičić, Y. Seo, S.-E. Takahasi and M. Tominaga, Inequalities of Furuta and Mond–Pečarić, Math. Ineq. Appl., 2 (1999), 83–111), we shall discuss complementary results to Jensen's type inequalities on the Hadamard product of positive ...

THE EQUIVALENCE OF CHEBYSHEV’S INEQUALITY TO THE HERMITE-HADAMARD INEQUALITY

2010

We prove that Chebyshev's inequality, Jensen's inequality and the Hermite-Hadamard inequality imply each other within the framework of probability measures. Some implications remain valid for certain classes of signed measures. By considering the case of semiconvex functions, we also prove a Kantorovich type variant of the Hermite-Hadamard inequality.

Some new inequalities of Hermite-Hadamard's type

Kyungpook Mathematical Journal, 2010

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

On Improvements of Kantorovich Type Inequalities

Mathematics, 2019

In the paper, we give some new improvements of the Kantorovich type inequalities by using Popoviciu’s, Hölder’s, Bellman’s and Minkowski’s inequalities. These results in special case yield Hao’s, reverse Cauchy’s and Minkowski’s inequalities.

On the Hermite-Hadamard type inequalities

Journal of Inequalities and Applications, 2013

In the present paper, we establish some new Hermite-Hadamard type inequalities involving two functions. Our results in a special case yield recent results on Hermite-Hadamard type inequalities. MSC: 26D15