AbstractLet p(z) = ∑v = 0navzv be a polynomial of degree n having no zeros in ¦z¦ < k, k ⩾ 1. Then we prove that for 1 ⩽ r ⩽ k, max¦z¦ = r ¦p′(z)¦ ⩽ n(r + k)n − 1(1 + k)n max¦z¦ = 1 ¦p(z)¦ and for 0 ⩽ r ⩽ λ ⩽ 1, max¦z¦ = r ¦p(z)¦ ⩾ (k + r)n(k + λ)n max¦z¦ = λ ¦p(z)¦. Both results are best possible. Besides, it has been shown that if in addition p′(0) = 0, then the bound in the latter inequality can be considerably improved
Let $p(z)$ be a polynomial of degree $n$ having no zero in $|z|< k$, $k\leq 1$, then Govil [Proc. Na...
AbstractLet P(z) = an Πnv=1 (z − zv), an ≠ 0 be a polynomial of degree n. It is known that if |zv| ≥...
AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥...
AbstractA well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z...
AbstractA well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z...
If pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989) proved maxz=1p...
Abstract. Let p(z) = a0 + ∑n j=t ajzj be a polynomial of degree n, having no zeros in |z | < k, ...
Abstract. Let p(z) = a0 + ∑n j=t ajzj be a polynomial of degree n, having no zeros in |z | < k, ...
Abstract. Let p(z) = a0 + ∑n j=t ajzj be a polynomial of degree n, having no zeros in |z | < k, ...
AbstractIf P(z)=∑ν=0ncνzν is a polynomial of degree n having no zeros in |z|<1, then for |β|⩽1, it w...
If p(z)=∑nv=0 avzv is a polynomial of degree n, having all its zeros in |z | ≤ 1, then it was prove...
n∑ v=µ an−vzn−v, 1 ≤ µ ≤ n, has all its zeros on |z | = k, k ≤ 1, then it was recently proved by De...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥...
Let $p(z)$ be a polynomial of degree $n$ having no zero in $|z|< k$, $k\leq 1$, then Govil [Proc. Na...
AbstractLet P(z) = an Πnv=1 (z − zv), an ≠ 0 be a polynomial of degree n. It is known that if |zv| ≥...
AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥...
AbstractA well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z...
AbstractA well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z...
If pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989) proved maxz=1p...
Abstract. Let p(z) = a0 + ∑n j=t ajzj be a polynomial of degree n, having no zeros in |z | < k, ...
Abstract. Let p(z) = a0 + ∑n j=t ajzj be a polynomial of degree n, having no zeros in |z | < k, ...
Abstract. Let p(z) = a0 + ∑n j=t ajzj be a polynomial of degree n, having no zeros in |z | < k, ...
AbstractIf P(z)=∑ν=0ncνzν is a polynomial of degree n having no zeros in |z|<1, then for |β|⩽1, it w...
If p(z)=∑nv=0 avzv is a polynomial of degree n, having all its zeros in |z | ≤ 1, then it was prove...
n∑ v=µ an−vzn−v, 1 ≤ µ ≤ n, has all its zeros on |z | = k, k ≤ 1, then it was recently proved by De...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥...
Let $p(z)$ be a polynomial of degree $n$ having no zero in $|z|< k$, $k\leq 1$, then Govil [Proc. Na...
AbstractLet P(z) = an Πnv=1 (z − zv), an ≠ 0 be a polynomial of degree n. It is known that if |zv| ≥...
AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥...
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