关于微分-差分多项式的单调函数

Abstract 在本文中，我们研究了关于微分-差分多项式的单调性：让 \(k_{1},k_{2},\cdots,k_{n}\) 是非负整数并且 \(k=\) max\(\{k_{1},k_{2},\cdots,k_{n}\}), 让 \(l\) 是 \(\{0,c_{1},c_{2},\cdots、c_{n}\}), let \(s\) be the number of distinct values of \(\{c_{1},c_{2},\cdots,c_{n}\}), let \(f(z)\) be a nonconstant meromorphic function of finite order satisfying （N(r、f)leq\frac{1}{8(lk+l+2s-1)+1}T(r,f)），让（m_{1}(z),m_{2}(z),\cdots,m_{n}(z),\）（a(z),b(z)）是（f(z)）的小函数，使得（a(z)\not\equiv b(z)），让（(c_{1}、k_{1}),(c_{2},k_{2}),\)\(\cdots,(c_{n},k_{n})\) be distinct and let \(F(z)=m_{1}(z)f^{(k_{1})}(z+c_{1})+m_{2}(z)f^{(k_{2})}(z+c_{2})+\cdots+m_{n}(z)f^{(k_{n})}(z+c_{n})\).如果 \(f(z)\) 和 \(F(z)\) 共享 \(a(z),b(z)\)CM，那么\(f(z)equiv F(z)\)。我们的结果改进并扩展了 [1, 18, 20] 的一些结果。