本文選題：Hyers-Ulam穩(wěn)定性　切入點(diǎn)：不動(dòng)點(diǎn)定理　出處：《曲阜師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：本文首先給出了三種不同二次可加泛函方程以及他們分別在不同的空間中的Hyers-Ulam穩(wěn)定性問題.我們采用的證明方法有直接法和不動(dòng)點(diǎn)法.根據(jù)內(nèi)容本文分為以下四章：第一章概述了一些本專業(yè)的基本知識(shí)及相關(guān)的理論淵源.第二章用不動(dòng)點(diǎn)方法證明了二次可加泛函方程在矩陣巴拿赫空間的穩(wěn)定性問題,其中,f：X→Y是一個(gè)映射,X是矩陣賦范空間,Y是矩陣巴拿赫空間.第三章證明了二次可加泛函方程此二次可加泛函方程為在巴拿赫空間的穩(wěn)定性問題,其中,f：X→Y是一個(gè)映射,X是賦范空間,Y是巴拿赫空間.第四章用不動(dòng)點(diǎn)方法證明了二次可加泛函方程在β.賦范左巴拿赫模上的穩(wěn)定性問題,這里n ≥2,f：X→Y是一個(gè)映射,X是β-賦范左B-模,Y是β-賦范左巴拿赫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，

本文編號(hào)：1611916