关于迭代方程sum from i=1 to ∞_((λ_if^i)(x))=F(x)的可微解

Discussion on the Differentiable Solutions of the Iterated Equation sum from i=1 to ∞_((λ_if^i)(x))=F(x)

通过构造新的算子,应用Schauder不动点定理讨论了闭区间[a,b]中一类包含无穷求和的、具有线性迭代形式的映射迭代方程的可微解的存在性与唯一性.

By constructing a structure operator quite different from that of [5] and using the Schauder fixed point theory, the existence and uniqueness of the differentiable solutions of the series-like iterative equations with variable coefficients are discussed.