Related papers: Tur\'an-type inequaities for generalized polygamma…
This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Same properties for the ratio of the modified Lommel functions with the Lommel function,…
Nicolas and DeSalvo and Pak proved that the partition function $p(n)$ is log concave for $n \geq 25$. Chen, Jia and Wang proved that $p(n)$ satisfies the third order Tur\'{a}n inequality, and that the associated degree 3 Jensen polynomials…
The first part of the paper is devoted to two descriptions of all polynomial tau-functions of the KP hierarchy: by a generalized Jacobi-Trudy formula, and a generalized Giambelli formula. We use the latter formula in the second part to…
The Tur\'{a}n inequalities and the higher order Tur\'{a}n inequalities arise in the study of Maclaurin coefficients of an entire function in the Laguerre-P\'{o}lya class. A real sequence $\{a_{n}\}$ is said to satisfy the Tur\'{a}n…
Using the multilinear theory of oscillatory integral operators, we establish a square function inequality with implications to moment inequalities for discrete exponential sums which frequencies lie on curved hyper-surfaces. In particular a…
In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…
A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…
Tur\'an problems in extremal combinatorics ask to find asymptotic bounds on the edge densities of graphs and hypergraphs that avoid specified subgraphs. The theory of flag algebras proposed by Razborov provides powerful methods based on…
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse…
Based on $k$-gamma and $k$-digamma functions, we show four series expansions to the Furdui-type integral related to Riemann zeta function and hypergeometric function, and also present some new identities, series expansions and inequalities…
In the paper, some lower bounds for polygamma functions are refined.
P. Tur\'an was the first to derive lower estimations on the uniform norm of the derivatives of polynomials $p$ of uniform norm $1$ on the interval I:=[-1,1] and the disk D:=$\{z \in C~:~|z| \le 1\}$, under the normalization condition that…
We show that recent multivariate generalizations of the Araki-Lieb-Thirring inequality and the Golden-Thompson inequality [Sutter, Berta, and Tomamichel, Comm. Math. Phys. (2016)] for Schatten norms hold more generally for all unitarily…
In this paper, we establish several new convex dominated functions and then we obtain new Hadamard type inequalities.
We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.
Inequalities among symmetric polynomial functions are fundamental questions in mathematics and have various applications in science and engineering. This paper investigates a beautiful and inspiring conjecture, proposed by Cuttler, Greene…
Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t=(t_1,t_2,...), leads to the standard Toda lattice and…
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.