Related papers: On Hilbert's sum type inequalities

We give some new relations for Newman digit sums respectively different modulos and put some problems. In particular, for the odd prime modulos we put an important conjecture.

In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved

Some new Gruss type inequalities in inner product spaces and applications for integrals are given.

In this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of split variational inequality problem, quasi-variational and variational inequality problems in Hilbert spaces. Using projection…

In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.

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.

The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.

The aim of this work is to present the first problems that appear in the study of nilpotent Leibniz superalgebras. These superalgebras and so the problems, will be considered as a natural generalization of nilpotent Leibniz algebras and Lie…

In this article, we focus on establishing a new variant of Hermite-Hadamard type inequalities for operator convex maps using an appropriate probability measure. To underline the usefulness of these inequalities, we investigate some…

We use the H\"{o}lder inequality for mixed exponents to prove some optimal variants of the generalized Hardy--Littlewood inequality for $m$-linear forms on $\ell _{p}$ spaces with mixed exponents. Our results extend recent results of Araujo…

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

We will establish the Caffarelli-Kohn-Nirenberg type inequalities with non-doubling weights being permitted. The classical Caffarelli-Kohn-Nirenberg type inequalities are categorized into non-critical and critical cases, and it is known…

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…

In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…

This short note contains elementary evaluations of some Euler sums.

The main results here are two Helly type theorems for the sum of (at most) unit vectors in a normed plane. Also, we give a new characterization of centrally symmetric convex sets in the plane.

In this paper, we establish Parseval identities and surprising new inequalities for weaving frames in Hilbert space, which involve scalar $\lambda\in\rs$. By suitable choices of $\lambda$, one obtains the previous results as special cases.…

Chen and Cheung [C.-P. Chen, W.-S. Cheung, Sharpness of Wilker and Huygens type inequalities, J. Inequal. Appl. 2012 (2012) 72, \url{http://dx.doi.org/10.1186/1029-242X-2012-72}] established sharp Wilker and Huygens-type inequalities. These…

We study an elementary inequality supporting the classical Hermite-Hadamard inequality in the matrix setting. This leads to a number of interesting matrix inequalities such new Schatten p-norm estimates and new majorization

In this paper, a new class of convex functions as a generalization of convexity which is called (h-m)-convex functions and some properties of this class is given. We also prove some Hadamard's type inequalities.