A new generalization of complex Stancu operators

Cetin N.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.16, pp.5582-5594, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 16
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5622
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5582-5594
  • Keywords: complex Stancu operator, convexity, exact order of approximation, spirallikeness, simultan approximation, starlikeness, univalence
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

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.