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On the q-Bernstein polynomials of the logarithmic function in the case q > 1

  • Sofiya Ostrovska EMAIL logo
Veröffentlicht/Copyright: 26. April 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 1

Abstract

The q-Bernstein basis used to construct the q-Bernstein polynomials is an extension of the Bernstein basis related to the q-binomial probability distribution. This distribution plays a profound role in the q-boson operator calculus. In the case q > 1, q-Bernstein basic polynomials on [0, 1] combine the fast increase in magnitude with sign oscillations. This seriously complicates the study of q-Bernstein polynomials in the case of q > 1.

The aim of this paper is to present new results related to the q-Bernstein polynomials Bn, q of discontinuous functions in the case q > 1. The behavior of polynomials Bn, q(f; x) for functions f possessing a logarithmic singularity at 0 has been examined.

Keywords: q-integers; q-binomial coefficients; q-Bernstein polynomials; convergence
MSC: Primary 26A15; 41A10

  1. This paper has been communicated by Stanisława Kanas.

Acknowledgement

I would like to express my sincere gratitude to Mr. P. Danesh from Atilim University Academic Writing and Advisory Centre for his help in the preparation of the manuscript.

References

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Received: 2012-10-22
Accepted: 2013-8-1
Published Online: 2016-4-26
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0116
Schlagwörter für diesen Artikel
q-integers; q-binomial coefficients; q-Bernstein polynomials; convergence

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
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  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
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  37. Research Article
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  41. Research Article
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  53. Research Paper
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