On the Stability of Jensen's Functional Equation on Groups

Proceedings Mathematical Sciences

Prasanna K Sahoo²  ValeriÄ­ A FaÄ­ziev¹ 

[1] Tver State Agricultural Academy, Tver Sakharovo, Russia$$;Department of Mathematics, University of Louisville, Louisville, KY 0, USA$$

关键词: Additive mapping;    Banach spaces;    Jensen equation;    Jensen function;    metabelian group;    metric group;    pseudoadditive mapping;    pseudo-Jensen function;    pseudocharacter;    quasiadditive map;    quasicharacter;    quasi-Jensen function;    semigroup;    direct product of groups;    stability of functional equation;    wreath product of groups.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper we establish the stability of Jensen’s functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and 𝑇(2,𝐾), where 𝐾 is an arbitrary commutative field with characteristic different from two. We also prove that any group 𝐴 can be embedded into some group 𝐺 such that the Jensen functional equation is stable on 𝐺.

【 授权许可】

Unknown