Naslov (eng)

On the Coincidence Theorem

Autor

Bakić, Radoš

Publisher

Opis (eng)

Abstract We are proving Coincidence theorem due to Walsh for the case when the total degree of a polynomial is less than the number of arguments. Also, the following result has been proven: if p(z) is a complex polynomial of degree n, then closed disk D that contains at least n−1 of its zeros (counting multiplicity) contains at least [ n − 2k + 1 2 ] zeros of its k-th derivative, provided that the arithmetical mean of these zeros is also centre of D. We also prove a variation of the classical composition theorem due to Szeg¨o.

Jezik

engleski

Datum

2024

Licenca

© All rights reserved

Predmet

Key words: Coincidence theorem, zeros of polynomial, critical points of a polynomial, apolar polynomials 2020 Mathematics Subject Classification: Primary 26C10, Secon- dary 30C15

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