Approximation Properties of the q-Balázs–Szabados Complex Operators in the Case q≥ 1

Mahmudov N.

Computational Methods and Function Theory, vol.16, no.4, pp.567-583, 2016 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 16 Say: 4
  • Nəşr tarixi: 2016
  • Doi nömrəsi: 10.1007/s40315-015-0154-7
  • jurnalın adı: Computational Methods and Function Theory
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.567-583
  • Açar sözlər: Complex q-Balázs–Szabados operators, Exact order of approximation, q-integer, Quantitative Voronovskaja-type formula
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

This paper deals with approximation properties of the newly defined q-generalization of the Balázs–Szabados complex operators in the case q≥ 1. Quantitative estimates of the convergence and Voronovskaja-type theorem are given. In particular, it is shown that the rate of approximation by the q-Balázs–Szabados (q> 1) is of order q- n β+ q- n ( 1 - β )(0<β≤23) versus 1 / n for the classical Balázs–Szabados (q= 1) operators. The results are new even for the classical case q= 1.