#### 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)

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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 $\Delta$.