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Convergence of generalized sampling series in weighted spaces

Acar Tuncer, Alagöz Osman, Aral Ali, Costarelli Danilo, Turgay Metin, Vinti Gianluca

Demonstratio Mathematica

2022

Vol. 55, nr 1

153--162

The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.

Approximation by q-analogue of modified Jakimovski-Leviatan-Stancu type operators

Mursaleen M., Nasiruzzaman M., Wafi A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

175--189

In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modied operators introduced by Atakut with the help of the q-Appell polynomials. We obtain some approximation results via the well-known Korovkin’s theorem for these operators. We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover, we study the rate of convergence in terms of modulus of continuity of these operators in a weighted space.

On weighted harmonic Bergman spaces

Petrosyan A.

Demonstratio Mathematica

2008

Vol. 41, nr 1

73-83

This paper is devoted to the investigation of the weighted Bergman harmonic spaces bp/alpha(B] in the unit ball in Rn. The reproducing kernel Ralpha for the ball is constructed and the integral representation for functions in bp/alpha(B) by means of this kernel is obtained. Besides an linear mapping between the bp/alpha(B) spaces and the ordinary L2-space on the unit sphere, which has an explicit form of integral operator along with its inversion, is established.