NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC FUNCTIONS WITH SHARED VALUES

Shyamali Dewan

  DOI:  https://doi.org/10.37418/jcsam.1.2.3

Full Text

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].

Keywords: Meromorphic functions, Normality criteria, Sharing values, Spherically locally uniformly convergence.