On the stability of a Jensen type functional equation on groups
Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 757-776
Published online 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
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd