The Properties of Differential-Difference Polynomials

The main aim of the 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) n f(z + c)](k) − α(z) and [f(z) n (f(z + c) − f(z))](k) − α(z) and give some examples to show that the results are best possible in a certain sense.