ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION  

作　　者：Iz-iddine EL-FASSI Janusz BRZDEK Abdellatif CHAHBI Samir KABBAJ 

机构地区：[1]Department of Mathematics,Faculty of Sciences,Ibn Tofail University,BP 133,Kenitra,Morocco [2]Department of Mathematics,Pedagogical University,Podchorazych 2,30-084 Krakow,Poland

出　　处：《Acta Mathematica Scientia》2017年第6期1727-1739,共13页数学物理学报（B辑英文版）

摘　　要：We present results on approximate solutions to the biadditive equationf（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.We present results on approximate solutions to the biadditive equationf（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 the-orem characterization of inner product space 

分 类 号：O175[理学—数学]