Some properties of solutions of complex $q$-shift difference equations
Combining difference and $q$-difference equations, we study the properties of meromorphic solutions of $q$-shift difference equations from the point of view of value distribution. We obtain lower bounds for the Nevanlinna lower order for meromorphic solutions of such equations. Our results improve and extend previous theorems by Zheng and Chen and by Liu and Qi. Some examples are also given to illustrate our results.