Related papers: A New Generalization of Chebyshev Inequality for R…

We establish point wise inequalities for Sobolev functions on a wider class of outward cuspidal domains. It is a generalization of an earlier result by the author and his collaborators

General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…

A novel method which is called the Chebyshev inertial iteration for accelerating the convergence speed of fixed-point iterations is presented. The Chebyshev inertial iteration can be regarded as a valiant of the successive over relaxation…

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…

The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.

We study weighted Chebyshev polynomials on compact subsets of the complex plane with respect to a bounded weight function. We establish existence and uniqueness of weighted Chebyshev polynomials and derive weighted analogs of Kolmogorov's…

An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…

A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the…

We show that, among all smooth one-dimensional maps conjugated to an N-ary shift (a Bernoulli shift of N symbols), Chebyshev maps are distinguished in the sense that they have least higher-order correlations. We generalise our consideration…

We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.

We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool.

In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability is modified. This modification can be understood as a…

The generalized complex numbers can be realized in terms of $2\times2$ or higher-order matrices and can be exploited to get different ways of looking at the trigonometric functions. Since Chebyshev polynomials are linked to the power of…

The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…

In this work a general relativistic generalization of Bell inequality is suggested. Namely,it is proved that practically in any general relativistic metric there is a generalization of Bell inequality.It can be satisfied within theories of…

We present new generalizations of Cauchy-Schwarz (CS) inequalities to multiple vectors and use them to derive multi-operator quantum uncertainty relations and propose multi-operator squeezing.

The aim of this paper is to generalize the Hermite--Hadamard inequality for functions convex on the coordinates. Our composite result generalizes the result of Dragomir in \cite{Drag}. Many other interesting inequalities can be derived from…