2017
Том 69
№ 5

All Issues

The properties on differential-difference polynomials

Cao T. B., Liu K., Liu X. L.


Abstract

The main aim of this paper is to improve some classical results on the distribution of zeros for differential polynomials and differential-difference polynomials. We present some results on the distribution of zeros of $[f(z)^nf(z + c)]^{(k)} \alpha (z)$ and $[f(z)^n(f(z + c) f(z))]^{(k)} \alpha (z)$ and give some examples to show that the results are best possible in a certain sense.

Citation Example: Cao T. B., Liu K., Liu X. L. The properties on differential-difference polynomials // Ukr. Mat. Zh. - 2017. - 69, № 1. - pp. 71-82.