Approximation by q-Durrmeyer type polynomials in compact disks in the case q > 1

Mahmudov N.

Applied Mathematics and Computation, vol.237, pp.293-303, 2014 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 237
  • Nəşr tarixi: 2014
  • Doi nömrəsi: 10.1016/j.amc.2014.03.119
  • jurnalın adı: Applied Mathematics and Computation
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.293-303
  • Açar sözlər: Complex q-Durrmeyer operators, Exact order of approximation, q-Beta function, q-Factorial, q-Integer, Quantitative Voronovskaja-type asymptotic formula
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

Recently, Agarwal and Gupta (2012) [1] studied some approximation properties of the complex q-Durrmeyer type operators in the case 01. More precisely, approximation properties of the newly defined generalization of this operators in the case q>1 are studied. Quantitative estimates of the convergence, the Voronovskaja type theorem and saturation of convergence for complex q-Durrmeyer type polynomials attached to analytic functions in compact disks are given. In particular, it is proved that for functions analytic in {zεℂ |z|q, the rate of approximation by the q-Durrmeyer type polynomials (q>1) is of order q-n versus 1/n for the classical (q=1) Durrmeyer type polynomials. Explicit formulas of Voronovskaya type for the q-Durrmeyer type operators for q>1 are also given. This paper represents an answer to the open problem initiated by Gal (2013) [6]. © 2014 Published by Elsevier Inc.