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Approximation of Discontinuous Functions by q-Bernstein Polynomials

In: Mathematical Analysis, Approximation Theory and Their Applications

Author

Listed:
  • Sofia Ostrovska

    (Atilim University)

  • Ahmet Yaşar Özban

    (Atilim University)

Abstract

This chapter presents an overview of the results related to the q-Bernstein polynomials with q > 1 attached to discontinuous functions on [0, 1]. It is emphasized that the singularities of such functions located on the set 𝕁 q : = { 0 } ∪ { q − l } l = 0 ∞ , q > 1 , $$\displaystyle{\mathbb{J}_{q}:=\{ 0\} \cup \{ q^{-l}\}_{ l=0}^{\infty },\;\;q> 1,}$$ are definitive for the investigation of the convergence properties of their q-Bernstein polynomials.

Suggested Citation

  • Sofia Ostrovska & Ahmet Yaşar Özban, 2016. "Approximation of Discontinuous Functions by q-Bernstein Polynomials," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 501-515, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31281-1_22
    DOI: 10.1007/978-3-319-31281-1_22
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