ON APPROXIMATELY ADDITIVE MAPPINGS IN 2-BANACH SPACES

被引：8

作者：

Brzdek, Janusz ^{[1
]}

El-Hady, El-Sayed ^{[2
,3
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, Mickiewicza 30, PL-30059 Krakow, Poland

[2] Jouf Univ, Coll Sci, Math Dept, POB 2014, Sakaka, Saudi Arabia

[3] Suez Canal Univ, Fac Comp & Informat, Basic Sci Dept, Ismailia 41522, Egypt

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2020年 / 101卷 / 02期

关键词：

Cauchy equation; Ulam stability; 2-Banach space; 2-norm; FUNCTIONAL-EQUATION; QUADRATIC MAPPINGS; STABILITY; HYPERSTABILITY; JENSEN;

D O I：

10.1017/S0004972719000868

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show how some Ulam stability issues can be approached for functions taking values in 2-Banach spaces. We use the example of the well-known Cauchy equation f (x + y) = f (x) + f (y), but we believe that this method can be applied for many other equations. In particular we provide an extension of an earlier stability result that has been motivated by a problem of Th. M. Rassias. The main tool is a recent fixed point theorem in some spaces of functions with values in 2-Banach spaces.

引用

页码：299 / 310

页数：12

共 29 条

[1] Stability of functional equations in single variable [J].

Agarwal, RP ;

Xu, B ;

Zhang, WN .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 288 (02) :852-869

[2]

[Anonymous], 2018, ULAM STABILITY OPERA

[3] Hyperstability of the Jensen functional equation [J].

Bahyrycz, A. ;

Piszczek, M. .

ACTA MATHEMATICA HUNGARICA, 2014, 142 (02) :353-365

[4] Hyperstability of general linear functional equation [J].

Bahyrycz, Anna ;

Olko, Jolanta .

AEQUATIONES MATHEMATICAE, 2016, 90 (03) :527-540

[5] On stability of the general linear equation [J].

Bahyrycz, Anna ;

Olko, Jolanta .

AEQUATIONES MATHEMATICAE, 2015, 89 (06) :1461-1474

[6] Hyperstability of the Cauchy equation on restricted domains [J].

Brzdek, J. .

ACTA MATHEMATICA HUNGARICA, 2013, 141 (1-2) :58-67

[7] ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS [J].

Brzdek, Janusz ;

Cieplinski, Krzysztof .

ACTA MATHEMATICA SCIENTIA, 2018, 38 (02) :377-390

[8] RECENT DEVELOPMENTS OF THE CONDITIONAL STABILITY OF THE HOMOMORPHISM EQUATION [J].

Brzdek, Janusz ;

Fechner, Wlodzimierz ;

Moslehian, Mohammad Sal ;

Sikorska, Justyna .

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2015, 9 (03) :278-326

[9] On Ulam's Type Stability of the Linear Equation and Related Issues [J].

Brzdek, Janusz ;

Cieplinski, Krzysztof ;

Lesniak, Zbigniew .

DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2014, 2014

[10]

Brzdek J, 2014, CARPATHIAN J MATH, V30, P47

← 1 2 3 →