R. Dalmasso

collaborators

3 papers

math.CV2023

A result related to the Sendov conjecture

Robert Dalmasso

The Sendov conjecture asserts that if $p (z) = \prod_{j = 1}^{N} (z - z_{j})$ is a polynomial with zeros $∣ z_{j} ∣ \leq 1$ , then each disk $∣ z - z_{j} ∣ \leq 1$ contains a zero of $p^{'}$ . Our purpos…

math.GM2023

A property of $C^{k, α}$ functions

Robert Dalmasso

Let $f$ be a nonnegative function of class $C^{k}$ ( $k \geq 2$ ) such that $f^{(k)}$ is H\''older continuous with exponent $α$ in $(0, 1]$ . If $f^{'} (x) = \dots = f^{(k)} (x) = 0$ when $f…

math.CA2018

On the Sendov conjecture for polynomials with simple zeros

Robert Dalmasso

The Sendov conjecture asserts that if all the zeros of a polynomial p lie in the closed unit disk then there must be a zero of p ' within unit distance of each zero. In this paper…

A result related to the Sendov conjecture

A property of Ck,α functions

On the Sendov conjecture for polynomials with simple zeros

A property of $C^{k, α}$ functions