一类多项式型迭代方程连续解的存在性

Existence of continuous solutions to one class of polynomial-like iterative equations

作者讨论了多项式型迭代方程(?)λ_if^i(x)=F(x)在λ_1>0,λ_i≤0,i=2,…,n,λ_i满足规范化条件(?)λ_i=1且F(x)连续递增,没有端点限制的情形下连续解的存在性,同时在一定条件下讨论了其解的唯一性、凸性和稳定性.

The existence of the solutions for a class of polynomial-like iterative equation ∑i=1^nλif^i（x）=F（x） is investigated, where λ1〉0,λi≤0,i=2,…,n,∑i=1^nλi=1 and F（x） is continuous and increasing without endpoint-fixed restriction. Meanwhile, the uniqueness, convexity and stability of the solutions are also discussed on certain conditions.