Approximation of Discontinuous Functions by q-Bernstein Polynomials

Sofia Ostrovska () and Ahmet Yaşar Özban ()
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Sofia Ostrovska: Atilim University
Ahmet Yaşar Özban: Atilim University

A chapter in Mathematical Analysis, Approximation Theory and Their Applications, 2016, pp 501-515 from Springer

Abstract: 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.

Keywords: q-Bernstein polynomial; Discontinuous function; Time scale; Convergence (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31281-1_22

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DOI: 10.1007/978-3-319-31281-1_22

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