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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; <

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.

Valeriĭ A Faĭziev¹ Prasanna K Sahoo²

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

Published

February 2007

Manuscript received

17 March 2005