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On the stability of Jensen’s functional equation on groups |
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| Authors: | Valeriĭ A Faĭziev Prasanna K Sahoo |
| Affiliation: | (1) Tver State Agricultural Academy, Tver Sakharovo, Russia;(2) Department of Mathematics, University of Louisville, Louisville, KY 40292, USA |
| 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. |
| 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 stability of functional equation, wreath product of groups |
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