A new generalization of complex Stancu operators. (10th April 2019)

• Record Type: Journal Article
• Authors: Çetin, Nursel
• Other Names: Yıldırım Kenan guestEditor.; Rasa Ioan guestEditor.; Acar Tuncer guestEditor.; Abazari Reza guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 16(2019)
• Page Start: 5582
• Page End: 5594
• Publication Date: 2019-04-10
• Subjects: complex Stancu operator -- convexity -- exact order of approximation -- spirallikeness -- simultaneous approximation -- starlikeness -- univalence; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5622
• Languages: English
• ISSNs: 0170-4214

Abstract

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.