Add to ORKGLet f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical point ζ of f with |f(ζ)/ζ| ≤ 1/2 provided that the critical points of f lie in the sector {re iθ:r > 0,|θ| ≤ π/6}, and |f(ζ)/ζ| < 2/3 if they lie in the union of the two rays {1+re±iθ:r ≥ 0}, where 0 < θ ≤ π /2. Copyright © 2010 Australian Mathematical Publishing Association Inc
This paper is devoted to the problem of where the critical points of a polynomial are relative to th...
AbstractThis paper is primarily concerned with complex polynomials which have critical points which ...
© 2019 American Mathematical Society. We prove the dual Smale's mean value conjecture for polynomial...
Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical p...
Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical p...
Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical p...
Abstract. Let f be a polynomial of degree n ≥ 2 with f(0) = 0 and f ′(0) = 1. We prove that there ...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Abstract. Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = {z: ...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Abstract. Let p(z) = (z − z1)(z − z2) (z − zn) be a polynomial whose zeros zk all lie in the ...
The well-known Sendov Conjecture asserts that if all the zeros of a polynomial p lie in the closed u...
Given a polynomial with complex coefficients, the celebrated Gauss-Lucas's theorem and Marden's theo...
This paper is devoted to the problem of where the critical points of a polynomial are relative to th...
AbstractThis paper is primarily concerned with complex polynomials which have critical points which ...
© 2019 American Mathematical Society. We prove the dual Smale's mean value conjecture for polynomial...
Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical p...
Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical p...
Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical p...
Abstract. Let f be a polynomial of degree n ≥ 2 with f(0) = 0 and f ′(0) = 1. We prove that there ...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Abstract. Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = {z: ...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′...
Abstract. Let p(z) = (z − z1)(z − z2) (z − zn) be a polynomial whose zeros zk all lie in the ...
The well-known Sendov Conjecture asserts that if all the zeros of a polynomial p lie in the closed u...
Given a polynomial with complex coefficients, the celebrated Gauss-Lucas's theorem and Marden's theo...
This paper is devoted to the problem of where the critical points of a polynomial are relative to th...
AbstractThis paper is primarily concerned with complex polynomials which have critical points which ...
© 2019 American Mathematical Society. We prove the dual Smale's mean value conjecture for polynomial...