arXiv subjects

Faton M. Berisha

Publications and source records attributed to Faton M. Berisha.

13 recordsLinked to original sources

arXiv2017

On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness

In this paper, we give a characterization of Nikol'ski\uı-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.

math.CA↗

arXiv2015

Some reverse $l_p$-type inequalities involving certain quasi monotone sequences

In this paper, we give some $l_p$-type inequalities about sequences satisfying certain quasi monotone type properties. As special cases, reverse $l_p$-type inequalities for non-negative decreasing sequences are obtained. The inequalities are closely related to Copson's and Leindler's inequalities, but the sign of the inequalities is reversed.

math.CA↗

arXiv2014

Approximating classes of functions defined by a generalised modulus of smoothness

In the present paper, we use a generalised shift operator in order to define a generalised modulus of smoothness. By its means, we define generalised Lipschitz classes of functions, and we give their constructive characteristics. Specifically, we prove certain direct and inverse types theorems in approximation theory for best approximation by algebraic polynomials.

math.FA↗

arXiv2012

A note on an inverse theorem for a generalised modulus of smoothness

We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.

math.FA↗

arXiv2012

On Jackson's theorem for the modulus of smoothness determined by a nonsymmetric generalised shift operator

In this paper a class of asymmetrical operators of generalised translation is introduced, for each of them generalised moduli of smoothness are introduced, and Jackson's and its converse theorems are proved for those moduli. ----- V etoǐ rabote rassmatrivaetsya klass sesimmetrichnykh operatorov obobshchenogo sdviga, dlya kazhdogo iz nikh vvoditsya obobshchennye moduli gladkosti i dlya nikh dokazybaetsya teorma Dzheksona i teorema, obratnaya eǐ.

math.FA↗

arXiv2012

On a connection between a generalised modulus of smoothness of order~$r$ and the best approximation by algebraic polynomials

In this paper an asymmetrical operator of generalised translation is introduced, the generalised modulus of smoothness is defined by its means and the direct and inverse theorems in approximation theory are proved for that modulus. ----- V dannoǐ rabote vvoditsya nesimmetrichnyǐ operator obobshchennogo sdviga, s ego pomoshchyu opredelyaetsya obobshchennyǐ modul' gladkosti i dlya nego dokazyvaetsya pryamaya i obratnaya teoremy teorii priblizheniǐ.

math.FA↗

arXiv2012

On some transforms of trigonometric series

We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.

math.NA↗

arXiv2012

On monotone Fourier coefficients of a function belonging to Nikol'ski\uı--Besov classes

In this paper, necessary and sufficient conditions on terms of monotone Fourier coefficients for a function to belong to a Nikol'ski\uı--Besov type class are given.

math.CA↗

arXiv2012

Direct and inverse theorems of approximation theory for a generalised modulus of smoothness

An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.

math.FA↗

arXiv2012

A theorem on approximation by algebraic polynomials of functions with given generalised modulus of smoothness

We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.

math.FA↗

arXiv2012

Approximation of classes of functions defined by a generalized $r$-th modulus of smoothness

In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of functions having given order of best approximation by algebraic polynomials.

math.FA↗

arXiv2012

Approximating classes of functions defined by operators of differentiation or operators of generalised translation by means of algebraic polynomials

In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of classes of functions defined by the order of best approximation by algebraic polynomials.

math.FA↗

arXiv2012

On coincidence of classes of functions defined by a generalised modulus of smoothness and the appropriate inverse theorem

We give the theorem of coincidence of a class of functions defined by a generalised modulus of smoothness with a class of functions defined by the order of the best approximation by algebraic polynomials. We also prove the appropriate inverse theorem in approximation theory.

math.FA↗