On the Conjecture of C. C. Yang and periodicity of meromorphic functions

In this paper, we investigate two recent conjectures posed by Yang concerning the periodicity of entire functions. A portion of these problems was recently addressed by Qiong and Peichu [Acta Math. Sci. Ser. B (Engl. Ed.) 38 (2018) 209-214] and Liu [Bull. Aust. Math. Soc. 101 (2020) 290-296], who provided partial solutions within the class of entire functions. The purpose of this work is to establish several new periodicity theorems that not only significantly improve the results of Qiong-Peichu and Liu, but also extend them to a much broader setting. Furthermore, we provide a series of illustrative examples to demonstrate the sharpness and validity of the hypotheses in our main results.