# ON THE STABILITY OF A JENSEN TYPE FUNCTIONAL EQUATION ON GROUPS

• FAIZIEV VALERH A. (TVER STATE AGRICULTURAL ACADEMY) ;
• SAHOO PRASANNA K. (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF LOUISVILLE)
• Published : 2005.11.01

#### 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, $\mathbb{C}$).

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