THE STABILITY OF A GENERALIZED AFFINE FUNCTIONAL EQUATION IN FUZZY NORMED SPACES

被引：3

作者：

Mursaleen, M. ^{[1
]}

Ansari, Khursheed J. ^{[2
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[2] King Khalid Univ, Coll Sci, Dept Math, Abha 61413, Saudi Arabia

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2016年 / 100卷 / 114期

关键词：

functional equation; Hyers-Ulam-Rassias stability; fuzzy normed space; fixed point alternative method;

D O I：

10.2298/PIM1614163M

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain the general solution of the following functional equation f (kx(1) + x(2) + ... + x(k))+ f (x(1)+ kx(2) + ... + xk) + ... + f(x(1)+ x(2) + ... + kx(k)) + f(x(1)) + f(x(2)) + ... + f(x(k)) = 2kf (x(1) + x(2) + ... + x(k)), k >= 2. We establish the Hyers-Ulam-Rassias stability of the above functional equation in the fuzzy normed spaces. More precisely, we show under suitable conditions that a fuzzy q-almost affine mapping can be approximated by an affine mapping. Further, we determine the stability of same functional equation by using fixed point alternative method in fuzzy normed spaces.

引用

页码：163 / 181

页数：19

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