Global smoothness and approximation by generalized discrete singular operators

Authors

  • George A. Anastassiou University of Memphis, USA
  • Merve Kester University of Memphis, USA

DOI:

https://doi.org/10.33993/jnaat432-1024

Keywords:

simultaneous global smoothness, simultaneous approximation with rates, generalized discrete singular operators, modulus of smoothness
Abstract views: 313

Abstract

In this article we continue with the study of generalized discrete singular operators over the real line regarding their simultaneous global smoothness preservation property with respect to \(L_{p}\) norm for \( 1\leq p\leq \infty ,\) by involving higher order moduli of smoothness. Additionally we study their simultaneous approximation to the unit operator with rates involving the modulus of smoothness. The Jackson type inequalities produced in this article are almost sharp, containing neat constants, and they reflect the high order of differentiability of involved function.

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References

U. Abel, Asymptotic expansions for the Favard operators and their left quasi-interpolants, Studia Univ. Babeş-Bolyai Math., 56 (2011) no. 2, pp. 199-206, http://www.cs.ubbcluj.ro/~studia-m/2011-2/abel-final.pdf

U. Abel and P.L. Butzer, Complete asymptotic expansion for generalized Favard operators, Constructive Approximation, 35 (2012), pp. 73-88, http://dx.doi.org/10.1007/s00365-011-9134-y DOI: https://doi.org/10.1007/s00365-011-9134-y

G.A. Anastassiou, On discrete Gauss-Weierstrass and Picard operators, Panamer. Math. J., 23 (2013) no. 2, pp. 79-86.

G.A. Anastassiou and M. Kester, Quantitative uniform approximation by generalized discrete singular operators, Studia Univ. Babeş-Bolyai Math., 60 (2015) no. 1, pp. 39-60, http://www.cs.ubbcluj.ro/~studia-m/2015-1/2015_1/05-anastassiou-final.pdf

G.A. Anastassiou and M. Kester, L_{p} approximation with rates by generalized discrete singular operators, Communications in Applied Analysis, accepted for publication, 2014. DOI: https://doi.org/10.1007/s00025-014-0412-4

G.A. Anastassiou and R.A. Mezei, Approximation by Singular Integrals, Cambridge Scientific Publishers, Cambrige, UK, 2012.

R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, Vol. 303, Berlin, New York, 1993. DOI: https://doi.org/10.1007/978-3-662-02888-9_10

J. Favard, Sur les multiplicateurs d'interpolation, J. Math. Pures Appl., IX, 23 (1944), pp. 219-247.

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Published

2014-08-01

How to Cite

Anastassiou, G. A., & Kester, M. (2014). Global smoothness and approximation by generalized discrete singular operators. Rev. Anal. Numér. Théor. Approx., 43(2), 113–140. https://doi.org/10.33993/jnaat432-1024

Issue

Vol. 43 No. 2 (2014)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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