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
收藏
页码：299 / 310
页数：12
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