We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
An Eneström-Kakeya theorem for new classes of polynomials.
- Authors
FRAZIER, WILLIAM "TY"; GARDNER, ROBERT
- Abstract
Consider the class of polynomials P(z) = Σnj=0 aj zj with 0 ≤ a0 ≤ a1 ≤ · · · ≤ an. The classical Eneström-Kakeya Theorem states that any polynomial in this class has all its zeros in the unit disk |z| ≤ 1 in the complex plane. We introduce new classes of polynomials by imposing a monotonicity-type condition on the coefficients with all indices congruent modulo m for some given m ≤ n. We give the inner and outer radii of an annulus containing all zeros of such polynomials. We also give an upper bound on the number of zeros in a disk for polynomials in these classes.
- Subjects
POLYNOMIALS; COMPLEX variables
- Publication
Acta et Commentationes Universitatis Tartuensis de Mathematica, 2019, Vol 23, Issue 1, p103
- ISSN
1406-2283
- Publication type
Article
- DOI
10.12697/ACUTM.2019.23.11