一类迭代函数方程组的C^m解的存在性和唯一性

Existence and Uniqueness of C^m Solutions for System of Iterative Functional Equations

讨论了较为广泛的一类迭代函数方程组G(x,f (x) ,… ,fn(x) ,g(x) ,… ,gn(x) ) =0H (x,g(x) ,… ,gn(x) ,f (x) ,… ,f n (x) ) =0 对任 x∈ J,其中 J为实数轴 R的连通闭子集 ,G,H∈ Cm(J2 n+ 1,R) ,n 2 .对任一个整数 m 0 ,本文在较弱的条件下证明了该方程组的 Cm解的存在性和唯一性 .

A relatively general kind of system of iterative functional equationsG(x,f(x),…,f n(x),g(x),…,g n(x))=0 H(x,g(x),…,g n(x),f(x),…,f n(x))=0 for any x∈Jis discussed, where J is a connected closed subset of the real number axis R, G,H∈C m(J 2n+1 , R), and n2. We prove the existence and uniqueness of C m solutions of the above system for any integer m0 under relatively weak conditions.