On the growth analysis of meromorphic solutions of finite logarithmic order of linear difference equations in the unit disc

The concept of logarithmic order in the unit disc forms a bridge between meromorphic functions of unbounded Nevanlinna characteristic and meromorphic functions of zero order of growth. In this paper, we investigate some growth properties of meromorphic solutions of higher order linear difference equation\begin{equation*}{A_n}(z)f(z + n) + \ldots + {A_1}(z)f(z + 1) + {A_0}(z)f(z) = 0,\end{equation*}where the coefficients A n (z),…, A 1 (z) and A 0 (z) are meromorphic functions of finite logarithmic order in the unit disc such that A n (z)A 0 (z) ≢ 0. Our result improves the results obtained by Belaidi (Math. Vesnik, 66 (2014), No. 2, 213-222).