We prove some results on the zeros of functions of the form f(z) = Σn=1∞ an/(z - zn), using quasiconformal surgery, Fourier series methods, and Baernstein's spread theorem. Our results have applications to fixpoints of entire functions.
Using the idea of weighted sharing we prove some theorems on uniqueness of meromorphic functions that share three values, which improve and supplement some results of Yi. Also we solve a problem recently raised by the present author [Austral. J. Math. Anal. Appl. 3 (2006)]. Examples are provided to show that some results are sharp.
In the paper we discuss the uniqueness problem for meromorphic functions that share two sets and prove five theorems which improve and supplement some results earlier given by Yi and Yang [13], Lahiri and Banerjee [5].
We study the uniqueness theorems of meromorphic functions concerning differential polynomials sharing a nonzero polynomial IM, and obtain two theorems which will supplement two recent results due to X. M. Li and L. Gao.
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.