Lp APPROXIMATION WITH RATES BY GENERALIZED DISCRETE SINGULAR OPERATORS

TitleLp APPROXIMATION WITH RATES BY GENERALIZED DISCRETE SINGULAR OPERATORS
Publication TypeJournal Article
Year of Publication2015
AuthorsAnastassiou, GA, KESTER, MERVE
Volume19
Issue2
Start Page217
Pagination18
Date Published2015
ISSN1083-2564
AMS26D15, 41A17, 41A25
Abstract

Here we give the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular operators. We treat both the unitary and non-unitary cases of the operators above. We derive quantitatively ${Lp}$ convergence of these operators to the unit operator by involving the ${Lp}$ higher modulus of smoothness of an ${ Lp(\mathbb{R}) }$ function.
URLhttp://www.acadsol.eu/en/articles/19/2/5.pdf
Refereed DesignationRefereed
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REFERENCES
[1] G. A. Anastassiou, Intelligent Mathematics: Computational Analysis, Springer, Heidelberg, New York, USA, 2011.
[2] G. A. Anastassiou, Approximation by Discrete Singular Operators, Cubo, Vol. 15, No.1 (2013), 97–112.
[3] G. A. Anastassiou and R. A. Mezei, Approximation by Singular Integrals, Cambridge Scientific Publishers, Cambrige, UK, 2012.
[4] G. A. Anastassiou and M. Kester, Quantitative Uniform Approximation by Generalized Discrete
Singular Operators, Submitted, 2013.
[5] R. A . DeVore and G. G. Lorentz, Constructive Approximation, Springer-Verlag, Vol. 303, Berlin, New York, 1993.
[6] J. Favard, Sur les multiplicateurs d’interpolation, J. Math. Pures Appl., IX, 23 (1944), 219–247.
[7] F. Smarandache, A triple inequality with series and improper integrals,
arxiv.org/ftp/mat/papers/0605/0605027.pdf, 2006.