Related papers: Inequalities of Levin-Ste\v{c}kin, Clausing and Ch…

We extend a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality.

Fe{j}\'er and Levin-Ste\v{c}kin inequalities treat integrals of the product of convex functions with symmetric functions. The main goal of this article is to present possible matrix versions of these inequalities. In particular,…

We use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type…

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the population of an arbitrary random vector X…

We address the optimal constants in the strong and the weak Stechkin inequalities, both in their discrete and continuous variants. These inequalities appear in the characterization of approximation spaces which arise from sparse…

In this paper we obtain some operator versions of Levin-Steckin integral inequality.

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

We obtain some new inequalities of Chebyshev Type.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

Recently Ohlin lemma on convex stochastic ordering was used to obtain some inequalities of Hermite-Hadamard type. Continuing this idea, we use Levin-Ste\v{c}kin result to determine all inequalities of the forms:…

Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type…

We give new necessary and sufficient conditions for higher order convex ordering. These results generalize the Levin-Ste\v{c}kin theorem (1960) on convex ordering. The obtained results can be useful in the study of the Hermite-Hadamard type…

In this paper, we obtain a new generalization of Chebyshev's inequality for random elements taking values in a separate Banach space.

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.

We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

We present inequalities and some applications to Kellers' limit and Carlemans' inequality.