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2012•Journal of MathematicsRequires access

MEROMORPHIC SOLUTIONS OF SYSTEM OF FUNCTIONAL EQUATIONS

Lingyun Gao

Open publisher page 3 citations

Abstract

This article investigates the problem of the growth and the exist of meromorphic solutions of system of functional equations of the form {f1n(cz)=a(z) (f_1~(m1)(z)/(f_2~(m2)(z)),f_2~ n(cz)=b(z)(f_2(m1)~(z))/(f_1~(m2)(z)),where a(z),b(z) are rational functions,|c|=0,1,n1,mi1(i=1,2).By using Nevanlinna theory of the value distribution of meromorphic functions and some methods of researching complex function equation,we obtain three results of the system of functional equations,which extend the results of function equation.

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What this paper is about

This article investigates the problem of the growth and the exist of meromorphic solutions of system of functional equations of the form {f1n(cz)=a(z) (f_1~(m1)(z)/(f_2~(m2)(z)),f_2~ n(cz)=b(z)(f_2(m1)~(z))/(f_1~(m2)(z)),where a(z),b(z) are rational functions,|c|=0,1,n1,mi1(i=1,2).By using Nevanlinna theory of the value distribution of meromorphic functions and some methods of researching complex function equation,we obtain three results of the system of functional equations,which extend the results of function equation.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This article investigates the problem of the growth and the exist of meromorphic solutions of system of functional equations of the form {f1n(cz)=a(z) (f_1~(m1)(z)/(f_2~(m2)(z)),f_2~ n(cz)=b(z)(f_2(m1)~(z))/(f_1~(m2)(z)),where a(z),b(z) are rational functions,|c|=0,1,n1,mi1(i=1,2).By using Nevanlinna theory of the value distribution of meromorphic functions and some methods of researching complex function equation,we obtain three results of the system of functional equations,which extend the results of function equation.

Key concepts: Meromorphic function, Mathematics, Functional equation, Nevanlinna theory, Function (biology), L-function, Rational function, Pure mathematics

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