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ON ZERO FREE REGIONS FOR DERIVATIVES OF A POLYNOMIAL.
- Source :
- Kragujevac Journal of Mathematics; 2023, Vol. 47 Issue 3, p403-407, 5p
- Publication Year :
- 2023
-
Abstract
- Let P<subscript>n</subscript> denote the set of polynomials of the form ... with |a| ≤ 1 and |z<subscript>k</subscript>| ≥ 1 for 1 ≤ k ≤ n - m. For the polynomials of the form p(z) = z∏<subscript>k=1</subscript><superscript>n-1</superscript>(z - z<subscript>k</subscript>), with |z<subscript>k</subscript>| ≥ 1, where 1 ≤ k ≤ n - 1, Brown [2] stated the problem "Find the best constant C<subscript>n</subscript> such that p'(z) does not vanish in |z| < Cn". He also conjectured in the same paper that C<subscript>n</subscript> = .... This problem was solved by Aziz and Zarger [1]. In this paper, we obtain the results which generalizes the results of Aziz and Zarger. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
PROBLEM solving
Subjects
Details
- Language :
- English
- ISSN :
- 14509628
- Volume :
- 47
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Kragujevac Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 164100351
- Full Text :
- https://doi.org/10.46793/KgJMat2303.403M