Normality and Uniqueness Property of Meromorphic Function in Terms of Some Differential Polynomials

In this paper, we will consider normality and uniqueness property of a family F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {F}$\end{document} of meromorphic functions when [Q(f)](k) and [Q(g)](k) share α ignoring multiplicities, for any f,g∈F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f,g\in \mathcal {F}$\end{document}, where Q is a polynomial and α is a small function. Our results do not need all of zeros of Q have large order as other authors’ results.