On the Periodicity of Entire Functions

The purpose of this paper is mainly to prove that if f is a transcendental entire function of hyper-order strictly less than 1 and f(z)n+a1f′(z)+⋯+akf(k)(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(z)^{n}+a_{1}f'(z)+\cdots +a_{k}f^{(k)}(z)$$\end{document} is a periodic function, then f(z) is also a periodic function, where n,  k are positive integers, and a1,⋯,ak\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{1},\cdots ,a_{k}$$\end{document} are constants. Meanwhile, we offer a partial answer to Yang’s Conjecture, theses results extend some previous related theorems.