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 $$f(z)^{n}+a_{1}f'(z)+\cdots +a_{k}f^{(k)}(z)$$ is a periodic function, then f(z) is also a periodic function, where n, k are positive integers, and $$a_{1},\cdots ,a_{k}$$ are constants. Meanwhile, we offer a partial answer to Yang’s Conjecture, theses results extend some previous related theorems.

中文翻译：

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关于整个函数的周期性

本文的目的主要是证明如果 f 是一个严格小于 1 的超阶的超越整函数且 $$f(z)^{n}+a_{1}f'(z)+\cdots + a_{k}f^{(k)}(z)$$是周期函数，那么f(z)也是周期函数，其中n、k为正整数，$$a_{1},\cdots ,a_{k}$$ 是常量。同时，我们对杨的猜想提供了部分答案，这些结果扩展了之前的一些相关定理。