ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

doi:10.1016/S0252-9602(17)30103-0

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (6): 1727-1739.doi: 10.1016/S0252-9602(17)30103-0

ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

Iz-iddine EL-FASSI¹, Janusz BRZD?K², Abdellatif CHAHBI³, Samir KABBAJ³

1. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 133, Kenitra, Morocco;
2. Department of Mathematics, Pedagogical University, Podchor??ych 2, 30-084 Kraków, Poland;
3. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 133, Kenitra, Morocco

收稿日期:2016-07-20 修回日期:2016-12-07 出版日期:2017-12-25 发布日期:2017-12-25
作者简介:Iz-iddine EL-FASSI,izidd-math@hotmail.fr;Janusz BRZDȨK,jbrzdek@up.krakow.pl;Abdellatif CHAHBI,abdellatifchahbi@gmail.com;Samir KABBAJ,samkabbaj@yahoo.fr

ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

Iz-iddine EL-FASSI¹, Janusz BRZD?K², Abdellatif CHAHBI³, Samir KABBAJ³

1. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 133, Kenitra, Morocco;
2. Department of Mathematics, Pedagogical University, Podchor??ych 2, 30-084 Kraków, Poland;
3. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP 133, Kenitra, Morocco

Received:2016-07-20 Revised:2016-12-07 Online:2017-12-25 Published:2017-12-25

摘要/Abstract

摘要：

We present results on approximate solutions to the biadditive equation
f(x + y, z-w) + f(x-y, z + w)=2f(x, z)-2f(y, w)
on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.

关键词: hyperstability, Ulam stability, biadditive functional equation, fixed point theorem, characterization of inner product space

Abstract:

Key words: hyperstability, Ulam stability, biadditive functional equation, fixed point theorem, characterization of inner product space

Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J]. 数学物理学报(英文版), 2017, 37(6): 1727-1739.

Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J]. Acta mathematica scientia,Series B, 2017, 37(6): 1727-1739.

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ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

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