Banach空间中迭代函数方程的凸解(英文)  

Convex Solutions of an Iterative Functional Equation in Banach Spaces

作　　者：龚小兵[1] 刘磊[2] 

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641100 [2]商丘师范学院数学与信息科学学院,河南商丘476000

出　　处：《四川师范大学学报（自然科学版）》2014年第3期341-347,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：supported by Key Project of Sichuan Provincial Department of Education(12ZA086)~~

摘　　要：迭代与迭代之间是有限线性组合关系的方程称为多项式型迭代方程,它是一类重要的泛函方程并被广泛研究.在Banach空间中研究了迭代与迭代之间是无限线性组合关系的迭代方程.利用Schauder不动点定理证明了此方程递增解和递减解的存在性.进一步给出了这些解为凸解或凹解的条件.结果推广了Banach空间中关于多项式型迭代方程凸解的结果.An iterative functional equation,in which the relation between iterate and iterate is finite linear combination,is called polynomial-like iterative equation,which is one of important forms of functional equations and is investigated widely.In this paper,we consider an iterative functional equation in which the relation between iterate and iterate is infinite linear combination in Banach spaces.By applying the Schauder＇ s fixed point theorem we investigate the existence of increasing solutions and decreasing solutions for this equation.Our results are generalization of convex solutions for the polynomial-like equation in Banach spaces.

关 键 词：函数方程 迭代 BANACH空间 序 增加算子 凸算子 

分 类 号：O193[理学—数学]