Related papers: On a Certain Function with Negative Coefficients

We prove pfaffian and hafnian versions of Lieb's inequalities on determinants and permanents of positive semi-definite matrices. We use the hafnian inequality to improve the lower bound of R\'ev\'esz and Sarantopoulos on the norm of a…

Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…

We establish a new improvement of the classical $L^p$-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one dimensional Hardy inequality.…

We prove the stronger version of Harnack's inequality for positive harmonic functions defined on the unit disc.

We prove an inequality that complements the famous Araki-Lieb-Thirring (ALT) inequality for positive matrices $A$ and $B$, by giving a lower bound on the quantity $\trace[A^r B^r A^r]^q$ in terms of $\trace[ABA]^{rq}$ for $0\le r\le 1$ and…

A now classical result in the theory of variable Lebesgue spaces due to Lerner [A. K. Lerner, On modular inequalities in variable $L^p$ spaces, Archiv der Math. 85 (2005), no. 6, 538-543] is that a modular inequality for the…

A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve…

Let G be a finite abelian group of order n. For a complex valued function f on G, let \fht denote the Fourier transform of f. The uncertainty inequality asserts that if f \neq 0 then |supp(f)| |supp(\fht)| \geq n. Answering a question of…

We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…

Let $$ T(q)=\sum_{k=1}^\infty d(k) q^k, \quad |q|<1, $$ where $d(k)$ denotes the number of positive divisors of the natural number $k$. We present monotonicity properties of functions defined in terms of $T$. More specifically, we proved…

For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on $\beta$ is determined so that $f$ is either starlike or convex of order $\alpha$. Several other…

In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence,…

As machine learning (ML) algorithms are used in applications that involve humans, concerns have arisen that these algorithms may be biased against certain social groups. \textit{Counterfactual fairness} (CF) is a fairness notion proposed in…

The goal of the article is to improve constants in the infimum convolution inequalities (IC for short) which were introduced by R. Lata{\l}a and J.O. Wojtaszczyk. We show that the exponential distribution satisfies IC with constant $2$ but…

For a real-valued non-negative and log-concave function we introduce a notion of difference function; the difference function represents a functional analog on the difference body of a convex body. We prove a sharp inequality which bounds…

In a generalization of the classical Hilbert inequality by Hardy, Littlewood and P\'{o}lya, the best constant for an inequality is determined provided that the generating function for the corresponding matrix satisfies certain monotonicity…

The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and…

Newton's inequalities $c_n^2 \ge c_{n-1}c_{n+1}$ are shown to hold for the normalized coefficients $c_n$ of the characteristic polynomial of any $M$- or inverse $M$-matrix. They are derived by establishing first an auxiliary set of…

We present an elementary proof of a conjecture proposed by I. Rasa in 2017 which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive by A. Komisarski and T. Rajba very recently by the use…

In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of…