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On the behaviour of derivative of algebraic polynomials in the regions with cusps.
- Source :
- Applied Mathematics in Science & Engineering; Dec2022, Vol. 30 Issue 1, p339-361, 23p
- Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
QUASICONFORMAL mappings
CUSP forms (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 27690911
- Volume :
- 30
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Applied Mathematics in Science & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 160934317
- Full Text :
- https://doi.org/10.1080/27690911.2022.2076844