Benharrat Belaidi, Mohammed Amin Abdellaoui, On the value distribution theory of differential polynomials in the unit disc, 2016 (2016), Article ID 16 (5 April 2016)

Full Text: PDF

Abstract

In this paper, we investigate the relationship between small functions and non-homogeneous differential polynomials $g_k=d_k(z)f^{(k)}+$ $\cdots +d_1(z) f^{\prime}$ $+d_0(z) f+b(z),$ where $d_0(z),$ $d_1(z),$ $\cdots,$ $d_k(z)$ and $b(z)$ are finite $[p,q]$ -order meromorphic functions in the unit disc $\Delta$ and $k\geq 2$ is an integer, which are not all equal to zero generated by the complex higher order non-homogeneous linear differential equation $f^{(k)}+A_{k-1}(z) f^{(k-1) } +\cdots$ $+A_1( z) f^{\prime}$ $+A_{0}(z) f =F,$ for $(k\geq 2) ,$ where $A_{0}(z), A_1(z),$ $\cdots,A_{k-1}(z)$ are finite $[p,q]$ -order meromorphic functions in unit disc $\Delta$ .

How to Cite this Article:

Benharrat Belaidi, Mohammed Amin Abdellaoui, On the value distribution theory of differential polynomials in the unit disc, Journal of Nonlinear Functional Analysis 2016 (2016), Article ID 16.