Value distribution of some $q$-difference polynomials

摘要

For a transcendental entire function $f(z)$ with zero order, the purpose of this article is to study the value distributions of $q$-difference polynomial $f(qz)-a(f(z))^{n}$ and $f(q_{1}z)f(q_{2}z)cdots f(q_{m}z)-a(f(z))^{n}.$ The property of entire solution of a certain $q$-difference equation is also considered.