A new generalization of complex Stancu operators

Cetin N.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.42, sa.16, ss.5582-5594, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 16
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1002/mma.5622
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.5582-5594
  • Anahtar Kelimeler: complex Stancu operator, convexity, exact order of approximation, spirallikeness, simultan approximation, starlikeness, univalence
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet

Özet

In this paper, we investigate approximation properties of the complex form of an extension of the Bernstein polynomials, defined by Stancu by means of a probabilistic method. We obtain quantitative upper estimates for simultaneous approximation and the exact order of approximation by these operators attached to analytic functions in closed disks. Also, we prove that the new generalized complex Stancu operators preserve the univalence, starlikeness, convexity, and spirallikeness in the unit disk.