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Abstract and Applied Analysis
Volume 2015, Article ID 915358, 11 pages
http://dx.doi.org/10.1155/2015/915358
Research Article

Quantitative Estimates for Positive Linear Operators in terms of the Usual Second Modulus

Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received 16 February 2015; Accepted 24 April 2015

Academic Editor: Milan Pokorny

Copyright © 2015 José A. Adell and A. Lekuona. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. A. Adell and J. de la Cal, “Bernstein-type operators diminish the φ-variation,” Constructive Approximation, vol. 12, no. 4, pp. 489–507, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. Z. Ditzian and V. Totik, Moduli of Smoothness, vol. 9 of Springer Series in Computational Mathematics, Springer, New York, NY, USA, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  3. Z. Finta, “Note on a Korovkin-type theorem,” Journal of Mathematical Analysis and Applications, vol. 415, no. 2, pp. 750–759, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. A. Özarslan and O. Duman, “Local approximation results for Szàsz-Mirakjan type operators,” Archiv der Mathematik, vol. 90, no. 2, pp. 144–149, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. Păltănea, Approximation Theory Using Positive Linear Operators, Birkhauser, Boston, Mass, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. Wang, C.-Y. Yang, and S. Duan, “Approximation order for multivariate Durrmeyer operators with Jacobi weights,” Abstract and Applied Analysis, vol. 2011, Article ID 970659, 12 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. A. Adell and C. Sangüesa, “Real inversion formulas with rates of convergence,” Acta Mathematica Hungarica, vol. 100, no. 4, pp. 293–302, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. Gonska and R. Păltănea, “Quantitative convergence theorems for a class of BErnstein-Durrmeyer operators preserving linear functions,” Ukrainian Mathematical Journal, vol. 62, no. 7, pp. 1061–1072, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. P. N. Agrawal, V. Gupta, and A. Sathish Kumar, “On q-analogue of Bernstein-Schurer-STAncu operators,” Applied Mathematics and Computation, vol. 219, no. 14, pp. 7754–7764, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. P. N. Agrawal, V. Gupta, A. S. Kumar, and A. Kajla, “Generalized Baskakov-Szász type operators,” Applied Mathematics and Computation, vol. 236, pp. 311–324, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. Bustamante, “Estimates of positive linear operators in terms of second-order moduli,” Journal of Mathematical Analysis and Applications, vol. 345, no. 1, pp. 203–212, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. H. H. Gonska and D. X. Zhou, “On an extremal problem concerning Bernstein operators,” Serdica Mathematical Journal, vol. 21, no. 2, pp. 137–150, 1995. View at Google Scholar · View at MathSciNet
  13. D. P. Kacsó, “Approximation by means of piecewise linear functions,” Results in Mathematics, vol. 35, no. 1-2, pp. 89–102, 1999. View at Publisher · View at Google Scholar · View at MathSciNet