TY - JOUR
AU - Bakić, Radoš
PY - 2024/03/31
Y2 - 2024/04/25
TI - On the Coincidence Theorem
JF - Proceedings of the Bulgarian Academy of Sciences
JA - C. R. Acad. Bulg. Sci.
VL - 77
IS - 3
SE - Mathematics
DO - 10.7546/CRABS.2024.03.01
UR - https://proceedings.bas.bg/index.php/cr/article/view/493
SP - 325–329
AB - <p>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 $$\left[\frac{n-2k+1}{2} \right]$$ 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 Szegö.</p>
ER -