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- Title
Polynomials with Critical Values on Intervals.
- Authors
Dubinin, V. N.
- Abstract
For polynomials P( z) with real coefficients having a fixed leading coefficient and satisfying the conditions P( z) ∈ [−1, 1] for z ∈ [−1, 1] and P( z) ∈ [−1, 1] if P′( z) = 0, we obtain new covering theorems, a Bernshtein-type inequality, and inequalities for the coefficients. The proofs are based on the use of univalent conformal mappings.
- Subjects
POLYNOMIALS; ALGEBRA; CONFORMAL mapping; MATHEMATICAL mappings; GEOMETRIC function theory
- Publication
Mathematical Notes, 2005, Vol 78, Issue 5/6, p768
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-005-0182-0