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 On the stability of a Jensen type functional equation on groups Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 757-776 Printed December 1, 2005 Valeriu i A. Fau iziev and Prasanna K. Sahoo Tver State Agricultural Academy, University of Louisville Abstract : In this paper we establish the stability of a Jensen type functional equation, namely $f(xy)-f(xy^{-1}) = 2f(y)$, on some classes of groups. We prove that any group $A$ can be embedded into some group $G$ such that the Jensen type functional equation is stable on $G$. We also prove that the Jensen type functional equation is stable on any metabelian group, $GL ( n, \mathbb{C} )$, $SL ( n, \mathbb{C} )$, and $T ( n, \mathbb{C})$. Keywords : additive mapping, Banach spaces, Jensen type equation, Jensen type function, metabelian group, metric group, pseduoadditive mapping, pseudojensen type function, quasiadditive map, quasijensen type function, direct product of groups, stability of functiona MSC numbers : Primary 20M15, 20M30, 39B82 Downloads: Full-text PDF