The Zeros and Nevanlinna Deficiencies for Some $q$-Shift Difference Differential Polynomials of Meromorphic Functions
Received:October 19, 2020  Revised:April 07, 2021
Key Word: Nevanlinna theory   $q$-shift difference differential   zero order
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11761035; 12161074), the Natural Science Foundation of Jiangxi Province (Grant No.20181BAB201001) and the Foundation of Education Department of Jiangxi Province (Grant Nos.GJJ190876; GJJ202303; GJJ201813; GJJ191042).
 Author Name Affiliation Xiumin ZHENG School of Mathematics and Statistics, Jiangxi Normal University, Jiangxi 330022, P. R. China Hongyan XU School of Mathematics and Statistics, Jiangxi Normal University, Jiangxi 330022, P. R. China School of Mathematics and Computer Science, Shangrao Normal University, Jiangxi 334001, 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 $\delta(\infty, f(z)^nf(qz+c)^m)$.