Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f...Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z +c) and forward differences △c^n f(z), n ∈ N^+.展开更多
Consider the difference Riccati equation f(z+1) =(A(z)f(z)+B(z))/(C(z)f(z)+D(z)),where A,B, C,D are meromorphic functions, we give its solution family with one-parameter H(f(z))={f_0(z),f(z)=((f_1(z)-f_0(z))(f_2(z)-f_...Consider the difference Riccati equation f(z+1) =(A(z)f(z)+B(z))/(C(z)f(z)+D(z)),where A,B, C,D are meromorphic functions, we give its solution family with one-parameter H(f(z))={f_0(z),f(z)=((f_1(z)-f_0(z))(f_2(z)-f_0(z)))/(Q(z)(f_2(z)-f_1(z))+(f_2(z)-f_0(z)))}, where Q(z) is any constant in C or any periodic meromorphic function with period 1, and f_0(z),f_1(z),f_2(z) are its three distinct meromorphic solutions.展开更多
In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E...In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E and F,yet obtain the same results for Theorems E and F.We also weaken the condition(1.4)of Theorems C and D.展开更多
基金supported by the Natural Science Foundation of Guangdong Province in China(2016A030310106)the National Natural Science Foundation of China(11801110,11771090,11761035,11871260)the Foundation of Guangzhou Civil Aviation College(17X0419)
文摘Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z +c) and forward differences △c^n f(z), n ∈ N^+.
基金supported by the National Natural Science Foundation of China(11771090,11761035,11871260)the Natural Science Foundation of Guangdong Province in China(2016A030310106,2016A030313745)
文摘Consider the difference Riccati equation f(z+1) =(A(z)f(z)+B(z))/(C(z)f(z)+D(z)),where A,B, C,D are meromorphic functions, we give its solution family with one-parameter H(f(z))={f_0(z),f(z)=((f_1(z)-f_0(z))(f_2(z)-f_0(z)))/(Q(z)(f_2(z)-f_1(z))+(f_2(z)-f_0(z)))}, where Q(z) is any constant in C or any periodic meromorphic function with period 1, and f_0(z),f_1(z),f_2(z) are its three distinct meromorphic solutions.
基金This work is supported by the National Natural Science Foundation of China(11771090,11871260,11761035,11801093,11801110).
文摘In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E and F,yet obtain the same results for Theorems E and F.We also weaken the condition(1.4)of Theorems C and D.
