On maximum modulus of polynomials and related entire functions with restricted zeros
نویسندگان
چکیده
منابع مشابه
Inequalities for products of zeros of polynomials and entire functions
Estimates for products of the zeros of polynomials and entire functions are derived. By these estimates, new upper bounds for the counting function are suggested. In appropriate situations we improve the Jensen inequality for the counting functions and the Mignotte inequality for products of the zeros of polynomials. Mathematics subject classification (2010): 26C10, 30C15, 30D20.
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Let f(z) := ∑n ν=0 aνz ν be a polynomial of degree n having no zeros in the open unit disc, and suppose that max|z|=1 |f(z)| = 1. How small can max|z|=ρ |f(z)| be for any ρ ∈ [0 , 1)? This problem was considered and solved by Rivlin [4]. There are reasons to consider the same problem under the additional assumption that f ′(0) = 0. This was initiated by Govil [2] and followed up by the present ...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2002
ISSN: 1331-4343
DOI: 10.7153/mia-05-07