Hyperstability of the Jensen functional equation

被引：72

作者：

Bahyrycz, A. ^{[1
]}

Piszczek, M. ^{[1
]}

机构：

[1] Pedag Univ, Dept Math, PL-30084 Krakow, Poland

来源：

ACTA MATHEMATICA HUNGARICA | 2014年 / 142卷 / 02期

关键词：

Jensen equation; hyperstability; fixed point theorem; ULAM-RASSIAS STABILITY; RESTRICTED DOMAINS;

D O I：

10.1007/s10474-013-0347-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present some observations on hyperstability for the Jensen equation on restricted domain. Namely, we show, under some weak natural assumptions, that functions satisfying the equation approximately (in some sense) must be actually solutions to it.

引用

页码：353 / 365

页数：13

共 10 条

[1] APPROXIMATELY ISOMETRIC AND MULTIPLICATIVE TRANSFORMATIONS ON CONTINUOUS FUNCTION RINGS [J].

BOURGIN, DG .

DUKE MATHEMATICAL JOURNAL, 1949, 16 (02) :385-397

[2] A fixed point approach to stability of functional equations [J].

Brzdek, Janusz ;

Chudziak, Jacek ;

Pales, Zsolt .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) :6728-6732

[3]

Cadariu L., 2003, J INEQUAL PURE APPL, V2

[4] On the stability of the linear functional equation [J].

Hyers, DH .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1941, 27 :222-224

[5]

Jung SM, 2010, J MATH INEQUAL, V4, P191

[6] Hyers-Ulam-Rassias stability of Jensen's equation and its application [J].

Jung, SM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (11) :3137-3143

[7]

Kominek Z., 1989, Demonstratio Math., V22, P499

[8] A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation [J].

Lee, YH ;

Jun, KW .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 238 (01) :305-315

[9]

Maksa G., 2001, Acta Math, V17, P107

[10] On the Ulam stability of Jensen and Jensen type mappings on restricted domains [J].

Rassias, JM ;

Rassias, MJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 281 (02) :516-524

← 1 →