• On the Stability of Jensen's Functional Equation on Groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/117/01/0031-0048

• # Keywords

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; <

• # Abstract

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.

• # Author Affiliations

1. Tver State Agricultural Academy, Tver Sakharovo, Russia
2. Department of Mathematics, University of Louisville, Louisville, KY 40292, USA

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019