MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.16, pp.5582-5594, 2019 (SCI-Expanded)
Article / Article
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Science Citation Index Expanded (SCI-EXPANDED), Scopus
complex Stancu operator, convexity, exact order of approximation, spirallikeness, simultan approximation, starlikeness, univalence
Ankara Haci Bayram Veli University Affiliated:
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.