On Ulam's Type Stability of the Cauchy Additive Equation

被引:4
作者
Brzdek, Janusz [1 ]
机构
[1] Pedag Univ, Dept Math, PL-30084 Krakow, Poland
来源
SCIENTIFIC WORLD JOURNAL | 2014年
关键词
FIXED-POINT APPROACH; FUNCTIONAL-EQUATIONS; HYERS; HYPERSTABILITY; MAPPINGS;
D O I
10.1155/2014/540164
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.
引用
收藏
页数:7
相关论文
共 37 条
  • [1] [Anonymous], STABILITY MAPPINGS H
  • [2] [Anonymous], 1998, Stability of Functional Equations in Several Variables
  • [3] Aoki T., 1950, J MATH SOC JAPAN, V2, P64, DOI [10.2969/jmsj/00210064, DOI 10.2969/JMSJ/00210064]
  • [4] Hyperstability of the Jensen functional equation
    Bahyrycz, A.
    Piszczek, M.
    [J]. ACTA MATHEMATICA HUNGARICA, 2014, 142 (02) : 353 - 365
  • [5] Brillouet-Belluot N., 2012, Abs. Appl. Anal, V2012, DOI [DOI 10.1155/2012/716936, 10.1155/2012/716936]
  • [6] Hyperstability of the Cauchy equation on restricted domains
    Brzdek, J.
    [J]. ACTA MATHEMATICA HUNGARICA, 2013, 141 (1-2) : 58 - 67
  • [7] Brzdek J., 2014, B AUSTR MATH SOC, V89
  • [8] Brzdek J., 1994, Stability of Mappings of Hyers-Ulam Type, P19
  • [9] Hyperstability and Superstability
    Brzdek, Janusz
    Cieplinski, Krzysztof
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2013,
  • [10] Remarks on hyperstability of the Cauchy functional equation
    Brzdek, Janusz
    [J]. AEQUATIONES MATHEMATICAE, 2013, 86 (03) : 255 - 267