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december 2014 Abel transforms of positive linear operators on weighted spaces
Mehmet Ünver
Bull. Belg. Math. Soc. Simon Stevin 21(5): 813-822 (december 2014). DOI: 10.36045/bbms/1420071855

Abstract

The classical Korovkin approximation theory deals with the convergence of a sequence of positive linear operators. When the sequence of positive linear operators does not converge it will be useful to use some summability methods. In this paper we use the Abel method, a sequence-to-function transformation, to study a Korovkin type approximation theorem for positive linear operators acting from a weighted space $C_{\rho_{1}}$ into a weighted space $B_{\rho_{2}}.$ Moreover using the modulus of continuity we also give rate of Abel convergence.

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Mehmet Ünver. "Abel transforms of positive linear operators on weighted spaces." Bull. Belg. Math. Soc. Simon Stevin 21 (5) 813 - 822, december 2014. https://doi.org/10.36045/bbms/1420071855

Information

Published: december 2014
First available in Project Euclid: 1 January 2015

zbMATH: 1308.41020
MathSciNet: MR3298479
Digital Object Identifier: 10.36045/bbms/1420071855

Subjects:
Primary: 40A05, 41A25, 41A36

Rights: Copyright © 2014 The Belgian Mathematical Society

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Vol.21 • No. 5 • december 2014
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