The zeros and Nevanlinna deficiencies for some $q$-shift difference differential polynomials of meromorphic functions
The zeros and Nevanlinna deficiencies for some $q$-shift difference differential polynomials of meromorphic functions
Received:October 19, 2020  Revised:March 31, 2021
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 Author Name Affiliation Address Hongyan Xu Shangrao Normal University 上饶师范学院数学与计算机学院 Xiumin Zheng Jiangxi Normal University Department of Mathematics, Jiangxi Normal University, Nanchan, Jiangxi, $330022$, P. R. China
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The first purpose of this paper is to study the properties on some $q$-shift difference differential polynomials of meromorphic functions, some theorems about the zeros of some $q$-shift difference-differential polynomials with more general forms are obtained. The second purpose of this paper is to investigate the properties on the Nevanlinna deficiencies for $q$-shift difference differential monomials of meromorphic functions, we obtain some relations among $\delta(\infty,f)$, $\delta(\infty,f')$, $\delta(\infty,f(z)^nf(qz+c)^mf'(z))$, $\delta(\infty,f(qz+c)^mf'(z))$ and $\delta(\infty, f(z)^nf(qz+c)^m)$.