几类可加泛函方程的稳定性

发布时间：2018-03-14 16:00

  本文选题：Hyers-Ulam稳定性　切入点：不动点定理　出处：《曲阜师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文首先给出了三种不同二次可加泛函方程以及他们分别在不同的空间中的Hyers-Ulam稳定性问题.我们采用的证明方法有直接法和不动点法.根据内容本文分为以下四章：第一章概述了一些本专业的基本知识及相关的理论渊源.第二章用不动点方法证明了二次可加泛函方程在矩阵巴拿赫空间的稳定性问题,其中,f：X→Y是一个映射,X是矩阵赋范空间,Y是矩阵巴拿赫空间.第三章证明了二次可加泛函方程此二次可加泛函方程为在巴拿赫空间的稳定性问题,其中,f：X→Y是一个映射,X是赋范空间,Y是巴拿赫空间.第四章用不动点方法证明了二次可加泛函方程在β.赋范左巴拿赫模上的稳定性问题,这里n ≥2,f：X→Y是一个映射,X是β-赋范左B-模,Y是β-赋范左巴拿赫B-模.
[Abstract]:In this paper, we first give three different quadratic additive functional equations and their Hyers-Ulam stability in different spaces. We use direct method and fixed point method. Chapter 1: chapter 1 summarizes some basic knowledge of the major and related theoretical sources. Chapter 2 proves the stability of quadratic additive functional equations in matrix Barnach space by fixed point method. Of which F: X. 鈫扽 is a mapping X is a matrix normed space Y is a matrix Barnach space. In Chapter 3, we prove that the quadratic additive functional equation is a stability problem in Barnach space, where f: X. 鈫扖hapter 4th proves the stability of quadratic additive functional equations on 尾. Normed left Barnabas modules by using fixed point method, where n 鈮，

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