NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC FUNCTIONS WITH SHARED VALUES
- 1 December 2015
- journal article
- Published by Union of Researchers of Macedonia in Journal of Computer Science and Applied Mathematics
- Vol. 1 (2), 45-48
- https://doi.org/10.37418/jcsam.1.2.3
Abstract
In this paper we have discussed normality criteria of a family of meromorphic functions. We have studied whether a family of meromorphic functions $\mathcal{F}$ is normal in $D$ if for a normal family $G$ and for each function $f\in \mathcal{F} $ there exists $g\in G$ such that $(f^{(k)})^n = a_i$ implies $(g^{(k)})^n = a_i$, $i=1,2,\ldots$ for two distinct non zero constants $a_i$ and $n (\ge 2)$, $k$ being positive integers. In this approach we have considered the functions with multiple zeros and multiple poles. We also have proved another result which improves the result of Yuan et al. [1].