On the behaviour of derivative of algebraic polynomials in the regions with cusps. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Özkartepe, N. P.
• Is Part Of: Applied mathematics in science and engineering. Volume 30:Issue 1(2022)
• Page Start: 339
• Page End: 361
• Publication Date: 2022-01-02
• Subjects: Algebraic polynomials -- quasiconformal mapping -- Dini-smooth curve; Primary 30A10 -- 30C10 -- Secondary 41A17; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2022.2076844
• Languages: English
• ISSNs: 2769-0911

Abstract

Abstract : In this paper, we study the behavior of derivatives of algebraic polynomials in bounded and unbounded regions of the complex plane. At the same time, both interior and exterior cusp points are allowed on the boundary of such regions. Bernstein-Walsh-type estimates are obtained for derivatives of algebraic polynomials in the specified region with corners for exterior points, as well as Markoff-type estimates for closure of the region. As a result, estimates are found for the derivatives of algebraic polynomials in the whole complex plane. It is also shown that the inequality for the closed region is exact in order for the given region.