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Parity is an important and easy to recognise property for meromorphic functions. On the parity of meromorphic functions, Liu, Liu and Korhonen [J Math Anal Appl 512(2022):126129] obtained some meaningful results. In this paper, we investigate the parity of a meromorphic function y(z) under the hypothesis that y(z)2n-2y(z)n is even. In addition, we discuss the relationship on the parity of a meromorphic function with its q-difference polynomials and differential expressions. For instance, we consider the parity of a meromorphic function y(z) under the assumption that y'(z)/ y(z)n and y(qz)/y(z)n are odd or even functions, where n is a positive integer. [ABSTRACT FROM AUTHOR]

In this paper, we study the unicity of meromorphic functions and their differential-difference polynomials. Our results improve some results due to Chen-Yi [Results Math 63 (2013):557-565], Chen-Xu [Open Math 18 (2020):211-215], Banerjee-Maity [Bull Korean Math Soc 58 (2021):1175-1192], and Narasimha-Shilpa [Adv Pure Appl Math 13 (2022):53-61] [ABSTRACT FROM AUTHOR]