AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥ Kν ≥ 1, 1 ≤ ν ≤ n, then for p ≥ 1,[formula] where [formula] and [formula] This inequality is best possible in the case Kν = 1, 1 ≤ ν ≤ n, and equality holds for the polynomial (z + 1)n. In this paper, we extend the above inequality to values of p ∈ [0, 1) and thus conclude that this inequality in fact holds for all p ≥ 0
AbstractLet 0 < p ≤ q ≤ ∞, 1 − 1/p + 1/q ≥ 0. We examine how large the Lp norm on [−1, 1] of the der...
AbstractWe examine how large the Lp norm on [−1, 1] of the derivative of a real algebraic polynomial...
AbstractA well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z...
AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥...
AbstractLet P(z) = an Πnv=1 (z − zv), an ≠ 0 be a polynomial of degree n. It is known that if |zv| ≥...
Let P(z) = an Πnν=1 (z - zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥ Kν ≥ 1,...
Let P(z) = an Πnν=1 (z - zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥ Kν ≥ 1,...
AbstractLet Pn(z) = an ∏nv = 1 (z − zv), an ≠ 0, be a polynomial of degree n. It has been proved tha...
AbstractLet Pn(z) = an ∏nv = 1 (z − zv), an ≠ 0, be a polynomial of degree n. It has been proved tha...
Let Pn(z) = an ∏nv = 1 (z - zv), an ≠ 0, be a polynomial of degree n. It has been proved that if |zv...
Let Pn(z) = an ∏nv = 1 (z - zv), an ≠ 0, be a polynomial of degree n. It has been proved that if |zv...
AbstractLet pn(z) be a polynomial of degree n and Dα{pn(z)} its polar derivative. It has been proved...
AbstractLet p(z) = ∑v = 0navzv be a polynomial of degree n having no zeros in ¦z¦ < k, k ⩾ 1. Then w...
If pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989) proved maxz=1p...
AbstractLet 0 < p ≤ q ≤ ∞, 1 − 1/p + 1/q ≥ 0. We examine how large the Lp norm on [−1, 1] of the der...
AbstractLet 0 < p ≤ q ≤ ∞, 1 − 1/p + 1/q ≥ 0. We examine how large the Lp norm on [−1, 1] of the der...
AbstractWe examine how large the Lp norm on [−1, 1] of the derivative of a real algebraic polynomial...
AbstractA well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z...
AbstractLet P(z) = an Πnν=1 (z − zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥...
AbstractLet P(z) = an Πnv=1 (z − zv), an ≠ 0 be a polynomial of degree n. It is known that if |zv| ≥...
Let P(z) = an Πnν=1 (z - zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥ Kν ≥ 1,...
Let P(z) = an Πnν=1 (z - zν), an ≠ 0 be a polynomial of degree n. It is known that if |zν| ≥ Kν ≥ 1,...
AbstractLet Pn(z) = an ∏nv = 1 (z − zv), an ≠ 0, be a polynomial of degree n. It has been proved tha...
AbstractLet Pn(z) = an ∏nv = 1 (z − zv), an ≠ 0, be a polynomial of degree n. It has been proved tha...
Let Pn(z) = an ∏nv = 1 (z - zv), an ≠ 0, be a polynomial of degree n. It has been proved that if |zv...
Let Pn(z) = an ∏nv = 1 (z - zv), an ≠ 0, be a polynomial of degree n. It has been proved that if |zv...
AbstractLet pn(z) be a polynomial of degree n and Dα{pn(z)} its polar derivative. It has been proved...
AbstractLet p(z) = ∑v = 0navzv be a polynomial of degree n having no zeros in ¦z¦ < k, k ⩾ 1. Then w...
If pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989) proved maxz=1p...
AbstractLet 0 < p ≤ q ≤ ∞, 1 − 1/p + 1/q ≥ 0. We examine how large the Lp norm on [−1, 1] of the der...
AbstractLet 0 < p ≤ q ≤ ∞, 1 − 1/p + 1/q ≥ 0. We examine how large the Lp norm on [−1, 1] of the der...
AbstractWe examine how large the Lp norm on [−1, 1] of the derivative of a real algebraic polynomial...
AbstractA well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z...
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