This note presents a Markov-type inequality for polynomials in two variables where the Chebyshev polynomials of the second kind in either one of the variables are extremal. We assume a bound on a polynomial at the set of even or odd Chebyshev nodes with the boundary nodes omitted and obtain bounds on its even or odd order directional derivatives in a critical direction. Previously, the author h...

We show that, given a histogram with n bins—possibly non-contiguous or consisting of single points—there exists a unique polynomial histopolant (polynomial of order n with bin averages equal to the histogram’s). We also present histopolating cardinal functions for histograms with contiguous bins. The Hodge star operator from the theory of differential forms is the mapping which puts kand (d − k...

The aim of the present paper is to extend the classical Hermite-Hadamard inequality to the case when the convexity notion is induced by a Chebyshev system.

Absboer -Robust stability conditions for low-order Schw polynomials are obtained. In McuLu, conditions for dewe n = 2, 3, 4, and 5 are explicitly obtained. These conditions relate to &&ty of the corner points for n = 2.3 and for corner and possible supplementary points for n = 4 and 5. Two countere-ples given in the literature are fully discussed in relation to the obtained conditions. Futme re...

Caution: These polynomials are referred to as w0, w1, w2, ... in Sections 5-8 of [1]. However, beginning with Section 9 of [1], Hazewinkel uses the notations w1, w2, w3, ... for some different polynomials (the so-called big Witt polynomials, defined by formula (9.25) in [1]), which are not the same as our polynomials w1, w2, w3, ... (though they are related to them: in fact, the polynomial wk t...

Using the KOF data at the annual level, we construct ten different composite indices for comparing the extent of globalization of 131 countries for eleven years, 1999-2009. We compare the different indices of globalization among themselves and also with the Dreher-KOF index of globalization and find that among the different indices the Dreher-Chebyshev index is the most representative one. Amon...

By considering a family of orthogonal polynomials generalizing the Tchebycheff polynomials of the second kind we refine the corresponding results of De Sainte-Catherine and Viennot on Tchebycheff polynomials of the second kind (Lecture Notes in Mathematics, vol. 1171, 1985, Springer-Verlag, 120). © 2003 Elsevier Science Ltd. All rights reserved.

The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization ...