2018
Том 70
№ 12

# The properties on differential-difference polynomials

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.