On [p, q]-order of growth of solutions of linear differential equations in the unit disc

The $ [p, q] $-order of growth of solutions of the following linear differential equations $ (**) $ is investigated, \begin{document}$ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{'}+A_{0}(z)f = 0, (**) $\end{document} where $ A_{i}(z) $ are analytic functions in the unit disc, $ i = 0, 1, ..., k-1 $. Some estimations of $ [p, q] $-order of growth of solutions of the equation $ (\ast*) $ are obtained when $ A_{j}(z) $ dominate the others coefficients near a point on the boundary of the unit disc, which is generalization of previous results from S. Hamouda.