Approximation by Complex Perturbed Bernstein-Type Operators

Acu A., BAŞCANBAZ TUNCA G.

RESULTS IN MATHEMATICS, cilt.75, sa.3, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00025-020-01244-x
  • Dergi Adı: RESULTS IN MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Complex Bernstein operator, perturbed Bernstein operator, quantitative estimates, simultaneous approximation, equivalence
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we consider complex form of a modified (perturbed) Bernstein operators attached to an analytic function in a disk of radius R > 1 centered at the origin. We obtain quantitative estimates of the convergence in compact disks and exact degree of simultaneous approximation with the help of upper estimates in quantitative form, and of lower estimates obtained from a qualitative Voronovskaja type result.