On the Ulam stability of Jensen and Jensen type mappings on restricted domains

被引：53

作者：

Rassias, JM ^{[1
]}

Rassias, MJ ^{[1
]}

机构：

[1] Natl & Capodistrian Univ Athens, Sect Math & Informat, Pedagog Dept, Athens 15342, Greece

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 281卷 / 02期

关键词：

Ulam stability problem; Hyers-Ulam stability; Ulam stability; approximately odd mapping; additivem of the first form; additive of the second form; Jensen equation; Jensen type equation; restricted domain;

D O I：

10.1016/S0022-247X(03)00136-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of "Jensen" and "Jensen type," and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：516 / 524

页数：9

共 25 条

[1]

ACZEL J, 1966, LECT FUNCTIONAL EQUA

[2]

[Anonymous], 1993, INT J MATH MATH SCI

[3]

[Anonymous], 1996, DEMONSTRATIO MATH

[4]

[Anonymous], 1994, GEOMETRY ANAL MECH

[5]

[Anonymous], COLLECTION MATH PROB

[6] CLASSES OF TRANSFORMATIONS AND BORDERING TRANSFORMATIONS [J].

BOURGIN, DG .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 57 (04) :223-237

[7]

Cholewa P. W., 1984, AEQUATIONES MATH, V27, P76, DOI DOI 10.1007/BF02192660

[8] ON THE STABILITY OF THE QUADRATIC MAPPING IN NORMED SPACES [J].

CZERWIK, S .

ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 1992, 62 :59-64

[9]

Drljevic H., 1984, PUBL I MATH BEOGRAD, V36, P111

[10]

Fenyo I., 1980, I LOMBARDO ACCAD S A, V114, P235

← 1 2 3 →