Approximation properties of bivariate complex q-Bernstein polynomials in the case q > 1

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Mahmudov N.

Czechoslovak Mathematical Journal, vol.62, no.2, pp.557-566, 2012 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 62 Say: 2
  • Nəşr tarixi: 2012
  • Doi nömrəsi: 10.1007/s10587-012-0029-2
  • jurnalın adı: Czechoslovak Mathematical Journal
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.557-566
  • Açar sözlər: modulus of continuity, q-Bernstein polynomials, Voronovskaja type theorem
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate q-Bernstein polynomials for a function analytic in the polydisc DR1 × DR2 = {z ∈ C: {pipe}Z{pipe} < R1} × {z ∈ C: {pipe}z{pipe} < R1} for arbitrary fixed q > 1. We give quantitative Voronovskaja type estimates for the bivariate q-Bernstein polynomials for q > 1. In the univariate case the similar results were obtained by S. Ostrovska: q-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232-255, and S. G. Gal: Approximation by Complex Bernstein and Convolution Type Operators. Series on Concrete and Applicable Mathematics 8. World Scientific, New York, 2009. © 2012 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.