Related papers: Inequalities in calculus: methods of prooving resu…
The Fenchel-Young inequality is fundamental in Convex Analysis and Optimization. It states that the difference between certain function values of two vectors and their inner product is nonnegative. Recently, Carlier introduced a very nice…
In this paper, we study inequalities involving polynomials and quasimodular forms. More precisely, we focus on the monotonicity of the functions of the form $t \mapsto t^m F(it)$ where $F$ is a quasimodular form and $m > 0$. As an…
In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert,…
In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.
The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev…
In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
Inequality indices are quantitative scores that gauge the divergence of wealth distributions in human societies from the "ground state" of pure communism. While inequality indices were devised for socioeconomic applications, they are…
These lecture notes are devoted to selected topics related to the uncertainty principle in harmonic analysis. Rather than attempting a systematic treatment, we emphasize only a number of both classical and deep manifestations of this…
In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions,…
In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
In a series of publications of the second author, including some with coauthors, globally strictly convex Tikhonov-like functionals were constructed for some nonlinear ill-posed problems. The main element of such a functional is the…
Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…
Our aim is to provide a short and self contained synthesis which generalise and unify various related and unrelated works involving what we call Phi-Sobolev functional inequalities. Such inequalities related to Phi-entropies can be seen in…