ON THE HYERS-ULAM STABILITY OF LINEAR MAPPINGS

被引：170

作者：

RASSIAS, TM ^{[1
]}

SEMRL, P ^{[1
]}

机构：

[1] UNIV LJUBLJANA,DEPT MATH,YU-61000 LJUBLJANA,SLOVENIA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1993年 / 173卷 / 02期

关键词：

D O I：

10.1006/jmaa.1993.1070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let E1 be a real normed vector space and E2 a real Banach space. S. M. Ulam posed the problem: When does a linear mapping near an approximately linear mapping f: E1 E2 exist? We give a new generalized solution to this problem. An example illustrates when the answer to this question is negative. The behaviour of bounded approximately additive mappings which do not satisfy Hyers-UIam stability is also investigated. © 1993 Academic Press, Inc.

引用

页码：325 / 338

页数：14

共 50 条

[1] ON THE HYERS-ULAM STABILITY OF APPROXIMATELY PEXIDER MAPPINGS
Belaid, Bouikhalene
Elhoucien, Elqorachi
Rassias, Themistocles M.
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2008, 11 (04): : 805 - 818
[2] On the asymptoticity aspect of Hyers-Ulam stability of mappings
Hyers, DH
Isac, G
Rassias, TM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (02) : 425 - 430
[3] On the Asymptoticity Aspect of Hyers-Ulam Stability of Quadratic Mappings
A Rahimi
A Najati
J-H Bae
Journal of Inequalities and Applications, 2010
[4] On the Asymptoticity Aspect of Hyers-Ulam Stability of Quadratic Mappings
Rahimi, A.
Najati, A.
Bae, J. -H.
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,
[5] HYERS-ULAM STABILITY OF GENERAL JENSEN TYPE MAPPINGS
Park, Choonkil
Lu, Gang
Zhang, Ruijun
Shin, Dong Yun
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2014, 17 (04) : 667 - 673
[6] ON THE HYERS-ULAM STABILITY OF PSI-ADDITIVE MAPPINGS
ISAC, G
RASSIAS, TM
JOURNAL OF APPROXIMATION THEORY, 1993, 72 (02) : 131 - 137
[7] Hyers-Ulam Stability of Linear Differential Equations
Murali, R.
Selvan, A. Ponmana
COMPUTATIONAL INTELLIGENCE, CYBER SECURITY AND COMPUTATIONAL MODELS: MODELS AND TECHNIQUES FOR INTELLIGENT SYSTEMS AND AUTOMATION, 2018, 844 : 183 - 192
[8] Hyers-Ulam stability of derivations and linear functions
Boros, Zoltan
Gselmann, Eszter
AEQUATIONES MATHEMATICAE, 2010, 80 (1-2) : 13 - 25
[9] On the Hyers-Ulam stability of the linear differential equation
Popa, Dorian
Rasa, Ioan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (02) : 530 - 537
[10] HYERS-ULAM STABILITY OF MAPPINGS FROM A RING A INTO AN A-BIMODULE
Oubbi, Lahbib
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2013, 28 (04): : 767 - 782

← 1 2 3 4 5 →