In this paper we show a new inequality that generalizes to the unit sphere Lebedev-Milin of exponentiation functions on circle. It may also be regarded as counterpart second in Szegö limit theorem Toeplitz determinants On other hand, is variant several classical inequalities Moser-Trudinger type sphere. The incorporates deviation center mass from origin into optimal Aubin for with centered at o...

We present approximation kernels for orthogonal expansions with respect to Bernstein-Szegö polynomials. The construction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein-Szegö polynomials.

Astract. We continue to investigate some classes of Szegö type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szegö to this setting.

The present study’s intention is to produce exact estimations of some problems involving logarithmic coefficients for functions belonging the considered subcollection B mathvariant="script">T mathvariant="normal">sin bounded turning class. Furthermore, class id...

In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szegö type theory of orthogonal polynomials in the unit circle for several noncommuting variables. Thus, we obtain the recurrence equations and Christoffel-Darboux formulas for Szegö polynomials in several noncommuting...

This paper deals with Szegö type limits for multiplication operators on L(R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators Tf using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class o...

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This utilized to develop new subfamilies of bi-univalent via principle subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on estimation coefficients |a?|(?=2,3) Fekete–Szegö inequality for belonging these...

The theory of means and their inequalities is fundamental to many fields including mathematics, statistics, physics, and economics.This is certainly true in the area of probability and statistics. There are large amounts of work available in the literature. For example, some useful results have been given by Shaked and Tong 1 , Shaked and Shanthikumar 2 , Shaked et al. 3 , and Tong 4, 5 . Motiv...