数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (6): 1349-1358.doi: 10.1016/S0252-9602(15)30059-X

• 论文 • 上一篇    下一篇

ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY

Anna BAHYRYCZ1, Krzysztof CIEPLINSKI2, Jolanta OLKO1   

  1. 1. Institute of Mathematics, Pedagogical University, Podchorazych 2, 30-084 Kraków, Poland;
    2. AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland
  • 收稿日期:2015-04-27 修回日期:2014-08-19 出版日期:2015-11-01 发布日期:2015-11-01
  • 通讯作者: Krzysztof CIEPLIŃSKI, E-mail: cieplin@agh.edu.pl E-mail:cieplin@agh.edu.pl
  • 作者简介:Anna BAHYRYCZ, E-mail: bah@up.krakow.pl;Jolanta OLKO, E-mail: jolko@up.krakow.pl

ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY

Anna BAHYRYCZ1, Krzysztof CIEPLINSKI2, Jolanta OLKO1   

  1. 1. Institute of Mathematics, Pedagogical University, Podchorazych 2, 30-084 Kraków, Poland;
    2. AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland
  • Received:2015-04-27 Revised:2014-08-19 Online:2015-11-01 Published:2015-11-01
  • Contact: Krzysztof CIEPLIŃSKI, E-mail: cieplin@agh.edu.pl E-mail:cieplin@agh.edu.pl

摘要:

In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.

关键词: multi-Cauchy-Jensen mapping, (generalized) Hyers-Ulam stability, Cauchy's functional equation, Jensen's functional equation, fixed point method

Abstract:

In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.

Key words: multi-Cauchy-Jensen mapping, (generalized) Hyers-Ulam stability, Cauchy's functional equation, Jensen's functional equation, fixed point method

中图分类号: 

  • 39B82