Stability of additive mappings in non-Archimedean fuzzy normed spaces

被引：41
作者：
Mirmostafaee, Alireza Kamel [1 ,2 ]
Moslehian, Mohammad Sal [1 ,2 ]
机构：
[1] Ferdowsi Univ Mashhad, Dept Pure Math, Mashhad 91775, Iran
[2] Ferdowsi Univ Mashhad, CEAAS, Mashhad 91775, Iran
来源：
FUZZY SETS AND SYSTEMS | 2009年 / 160卷 / 11期
关键词：
Fuzzy stability; Cauchy equation; Jensen equation; Fuzzy norm; Non-Archimedean fuzzy normed space; ULAM-RASSIAS STABILITY; FUNCTIONAL-EQUATIONS;
D O I：
10.1016/j.fss.2008.10.011
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers-Ulam-Rassias-Gavruta. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces and the theory of functional equations. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：1643 / 1652
页数：10
相关论文
共 41 条
[1]  
[Anonymous], 1998, Stability of Functional Equations in Several Variables
[2]  
[Anonymous], PROBLEMS MODERN MATH
[3]  
Aoki T., 1950, J. Math. Soc. Japan, V2, P64
[4]   Fuzzy bounded linear operators [J].
Bag, T ;
Samanta, SK .
FUZZY SETS AND SYSTEMS, 2005, 151 (03) :513-547
[5]  
Bag T., 2003, J FUZZY MATH, V11, P687
[6]  
Cheng S. C., 1994, B CALCUTTA MATH SOC, V86, P429
[7]  
Czerwik Stefan, 2002, Functional Equations and Inequalities in Several Variables, P4
[8]   On the stability of Jensen's functional equation on groups [J].
Faiziev, Valerii A. ;
Sahoo, Prasanna K. .
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2007, 117 (01) :31-48
[9]   FINITE DIMENSIONAL FUZZY NORMED LINEAR-SPACE [J].
FELBIN, C .
FUZZY SETS AND SYSTEMS, 1992, 48 (02) :239-248
[10]   A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF APPROXIMATELY ADDITIVE MAPPINGS [J].
GAVRUTA, P .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 184 (03) :431-436
12345