Related papers: Inequalities for multiplicative arithmetic functio…

This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…

Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.

We deduce asymptotic formulas for the alternating sums $\sum_{n\le x} (-1)^{n-1} f(n)$ and $\sum_{n\le x} (-1)^{n-1} \frac1{f(n)}$, where $f$ is one of the following classical multiplicative arithmetic functions: Euler's totient function,…

Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.

We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…

In this paper we define an addition operation on the class of quasi-concave functions. While the new operation is similar to the well-known sup-convolution, it has the property that it polarizes the Lebesgue integral. This allows us to…

In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.

We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly…

The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.

In this paper we study properties of hyperholomorphic functions on commutative finite algebras. It is investigated the Cauchy-Riemann type conditions for hyperholomorphic functions. We prove that a hyperholomorphic function on a commutative…

In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.

This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…

We investigate the Hardy and Rellich inequalities for classes of antisymmetric and odd functions and general exponent $p$. The obtained constants are better than the classical ones.

We study flat deformations of quotients of a polynomial algebra in a class of graded commutative associative algebras. Functional equations and their solutions in terms of theta functions play important role in these studies. An analog of…

We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new…

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…

In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.

Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…