Approximation by a complex q-durrmeyer type operator

Gal S. G., Gupta V., Mahmudov N.

Annali dell'Universita di Ferrara, vol.58, no.1, pp.65-87, 2012 (Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 58 Say: 1
  • Nəşr tarixi: 2012
  • Doi nömrəsi: 10.1007/s11565-012-0147-7
  • jurnalın adı: Annali dell'Universita di Ferrara
  • Jurnalın baxıldığı indekslər: Scopus
  • Səhifə sayı: pp.65-87
  • Açar sözlər: Complex simultaneous approximation, q-Durrmeyer operators, Vo-ronovskaja-type result
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

Very recently, for 0 < q < 1 Govil and Gupta [10] introduced a certain q-Durrmeyer type operators of real variable x ∈ [0,1] and established some approximation properties. In the present paper, for these q-Durrmeyer operators, 0 < q < 1, but of complex variable z attached to analytic functions in compact disks, we study the exact order of simultaneous approximation and a Voronovskaja kind result with quantitative estimate. In this way, we put in evidence the overconvergence phenomenon for these q-Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from the real interval [0, 1] to compact disks in the complex plane. For q = 1 the results were recently proved in Gal-Gupta [8]. © 2012 Università degli Studi di Ferrara.