Related papers: Improving Schwarz Inequality in Inner Product Spac…
Schur's inequality for the sum of products of the differences of real numbers states that for $x,y,z,t\geq 0$, $x^t(x-y)(x-z) + y^t(y-z)(y-x) + z^t(z-x)(z-y) \geq 0$. In this paper we study a generalization of this inequality to more terms,…
We correct the proof of Theorem~8 in [\emph{Weak product spaces of Dirichlet series}, Integral Equations Operator Theory \textbf{86} (2016), no.~4, 453--473.]
In this short note, we improve the famous Reid Inequality related to linear operators.
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
The present note is an essential addition to the author's arxiv paper arXiv:2001.01070, concerning general multiplicative systems of random variables. Using some lemmas and the methodology of \cite{Kar4}, we obtain a general extreme…
Keller packings and tilings of boxes are investigated. Certain general inequality measuring a complexity of such systems is proved. A straightforward application to the unit cube tilings is given.
This paper establishes a sharp Schwarz-Pick type inequality for real-valued invariant harmonic functions defined on the complex unit ball $\mathbb B^n$. The proof of this main result simultaneously provides a solution to a natural extension…
Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem instead of simply doing time stepping for computing European…
This article discusses classical versions of the Schwarz lemma at the boundary of the unit disk in the complex plane. The exposition includes commentary on the history, the mathematics, and the applications.
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
A minor improvement is made to the calculation of the inhomogeneity term. The new calculation gives better agreement with the observations of Daoud et al. and Cheng-Graessley-Melnichenko.
The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy-Rellich…
Schur's inequality states that the sum of three special terms is always nonnegative. This note is a short review of inequalities for the sum of the reciprocals of these terms and of extensions of the latter inequalities to an arbitrary…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.
We introduce in this paper a new tool to prove the convergence of the Overlapping Optimized Schwarz Methods with multisubdomains. The technique is based on some estimates of the errors on the boundaries of the overlapping strips. Our…
We significantly improve our results of Glas. Mat., III. Ser. 53(2018), No. 2, 229-238, reducing relative Thue inequalities to absolute ones.
Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed…
We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea. We show that this also adapts to give some new sieve inequality for modular…
Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other…