AbstractIf p(z) is a polynomial of degree at most n having no zeros in ¦z¦ < 1, then according to a well known result conjectured by Erdős and proved by Lax max¦z¦ = 1 ¦p′(z)¦ ⩽ (n2) max¦z¦ = 1 ¦p(z)¦. On the other hand, by a result due to Turan, if p(z) has all its zeros in ¦z¦ ⩽ 1, then max¦z¦ = 1 ¦p′(z)¦ ⩾ (n2) max¦z¦ = 1 ¦p(z)¦. In this paper we generalize and sharpen these inequalities
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
AbstractLet p(z) = ∑v = 0navzv be a polynomial of degree n having no zeros in ¦z¦ < k, k ⩾ 1. Then w...
AbstractLet pn(z) = an Πv = 1n (z − zv), an ≠ 0 be a polynomial of degree n and let ∥pn∥ = max¦z¦ = ...
AbstractLet p(z) = ∑nv = 0 avzv be a polynomial of degree n and let M(p, r) = max¦z¦ = r ¦p(z)¦. It ...
Let $p(z)$ be a polynomial of degree $n$ having no zero in $|z|< k$, $k\leq 1$, then Govil [Proc. Na...
Let P(z) be a polynomial of degree n not vanishing in |z| 1 |P(z)| in terms of R,n,k, max|z|=1 |P(z)...
Let f(z) be an arbitrary entire function and M(f,r) = max|z|=r |f(z)|. For a polynomial p(z) of degr...
Let P(z) be a polynomial of degree n and for a complex number , let DP(z) = nP(z) + (alpha − z) P′(z...
Let P(z) be a polynomial of degree n and for a complex number , let DP(z) = nP(z) + (alpha − z) P′(z...
This paper deals with the problem of finding some upper bound estimates for the maximum modulus of t...
The Erdős–Lax Theorem states that if $P(z)=\sum _{\nu =1}^n a_{\nu }z^{\nu }$ is a polynomial of deg...
Let P(z) be a polynomial of degree n not vanishing in |z| 1 |P(z)| in terms of R,n,k, max|z|=1 |P(z)...
AbstractIn this paper we obtainLp,p≥1, inequalities for the class of polynomials having no zeros in ...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
AbstractLet p(z) = ∑v = 0navzv be a polynomial of degree n having no zeros in ¦z¦ < k, k ⩾ 1. Then w...
AbstractLet pn(z) = an Πv = 1n (z − zv), an ≠ 0 be a polynomial of degree n and let ∥pn∥ = max¦z¦ = ...
AbstractLet p(z) = ∑nv = 0 avzv be a polynomial of degree n and let M(p, r) = max¦z¦ = r ¦p(z)¦. It ...
Let $p(z)$ be a polynomial of degree $n$ having no zero in $|z|< k$, $k\leq 1$, then Govil [Proc. Na...
Let P(z) be a polynomial of degree n not vanishing in |z| 1 |P(z)| in terms of R,n,k, max|z|=1 |P(z)...
Let f(z) be an arbitrary entire function and M(f,r) = max|z|=r |f(z)|. For a polynomial p(z) of degr...
Let P(z) be a polynomial of degree n and for a complex number , let DP(z) = nP(z) + (alpha − z) P′(z...
Let P(z) be a polynomial of degree n and for a complex number , let DP(z) = nP(z) + (alpha − z) P′(z...
This paper deals with the problem of finding some upper bound estimates for the maximum modulus of t...
The Erdős–Lax Theorem states that if $P(z)=\sum _{\nu =1}^n a_{\nu }z^{\nu }$ is a polynomial of deg...
Let P(z) be a polynomial of degree n not vanishing in |z| 1 |P(z)| in terms of R,n,k, max|z|=1 |P(z)...
AbstractIn this paper we obtainLp,p≥1, inequalities for the class of polynomials having no zeros in ...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
Let $P_m$ be a class of all polynomials of degree at most m and let $R_{m,n}=R_{m,n}(d_{1}, ..., d_{...
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