Meromorphic functions that share one value with their derivatives.
We apply Nevanlinna's value distribution theory to show that some functional equations of Diophantine type have no admissible meromorphic solutions. This result confirms a recent conjecture of Li and Yang.
We establish a q-shift difference analogue of the logarithmic derivative lemma. We also investigate the value distributions of q-shift difference polynomials and the growth of solutions of complex q-shift difference equations.