﻿ 多元二次函数方程在限制定义域上的稳定性 The Stability of a Multi-Quadratic Functional Equation on a Restricted Domain

Operations Research and Fuzziology
Vol.06 No.04(2016), Article ID:18805,8 pages
10.12677/ORF.2016.64014

The Stability of a Multi-Quadratic Functional Equation on a Restricted Domain

Lin Wang1, Peisheng Ji2, Weiwei Liu2

1College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao Shandong

2School of Mathematics and Statistics, Qingdao University, Qingdao Shandong

Received: Oct. 8th, 2016; accepted: Oct. 24th, 2016; published: Oct. 27th, 2016

ABSTRACT

In this paper, we obtain the stability of the multi-quadratic functional equation on a restricted domain.

Keywords:Hyers-Ulam Stability, Functional Equation, Multi-Quadratic Functional Equation

1青岛科技大学数理学院，山东 青岛

2青岛大学数学与统计学院，山东 青岛

1. 引言

2. 主要结果及证明

(2.1)

，函数满足不等式

(2.2)

，且对，如果，那么中至少有一个元素为0，则存在唯一的多元二次函数使得

(2.3)

I. 首先证明对

。如果，当时，令，当时，令，显然有，

。 (2.4)

(2.5)

(2.6)

，如果，取。否则，当时，令，当。显然有，

(2.7)

(2.8)

II. 证明(2.3)式成立。

(2.9)

(2.10)

III. 证明函数是多元二次的。

(2.11)

IV. 证明函数是唯一的。

,

The Stability of a Multi-Quadratic Functional Equation on a Restricted Domain[J]. 运筹与模糊学, 2016, 06(04): 107-114. http://dx.doi.org/10.12677/ORF.2016.64014

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