一类多项式型迭代方程的高阶强凸解
Higher Order Strongly Convex Solutions to a Polynomial-like Iterative Functional Equation
张中月 1赵侯宇1
作者信息
摘要
利用Schauder不动点定理和Banach压缩映像原理讨论了 一类多项式型迭代函数方程的高阶强凸解的存在性、唯一性和稳定性.即一类多项式型迭代函数方程λ1f(x)+λ2f2(x)+…+λnfn(x)=F(x),∀x ∈ R在一定条件下有高阶强凸解,且解是唯一的,该解连续依赖于给定的函数F.
Abstract
By the Schauder's fixed point theorem and the Banach contraction principle,the paper finds that higher order strongly convex solutions to polynomial iterative functional equation are existing,unique and stable.That is,under some con-ditions,the polynomial iterative functional equation has the higher order strongly convex solutions.λ1 f(x)+λ2 f2(x)+…+λnfn(x)=F(x),∀x ∈ R.And the solution is an unique one which depends on the given function F.
关键词
迭代函数方程/高阶强凸/不动点Key words
iterative functional equation/higher order strongly convex/fixed point引用本文复制引用
出版年
2024
NETL
NSTL
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