On polynomials whose zeros are in the unit disk
نویسندگان
چکیده
منابع مشابه
Some Families of Graphs whose Domination Polynomials are Unimodal
Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.
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Let Q be a real polynomial of degree N all of whose zeros lie in the half-plane Re z < 0. Let M(r, Q) be the maximum of | Q(z) | on \z\= r and n(r,0) the counting function of the zeros of Q. It is shown that the inequality M(r, Q') « (2r)"'{A' + n(r,0)}M(r, Q) holds for r > 0. It is also shown that Bernstein's inequality characterizes polynomials.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1971
ISSN: 0022-247X
DOI: 10.1016/0022-247x(71)90045-x