In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some o
f the results of Fang and Zalcman and Chen et al to a great extent.
In this paper, we obtained some normality criteria for families of holomorphic functions. Which generalizes some results of Fang, Xu, Chen and Hua.
It is known that the dynamics of $f$ and $g$ vary to a large extent from that of its composite entire functions. Using Approximation theory of entire functions, we have shown the existence of entire functions $f$ and $g$ having infinite number of dom
ains satisfying various properties and relating it to their composition. We have explored and enlarged all the maximum possible ways of the solution in comparison to the past result worked out.
