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2007 On the stability of Drygas functional equation on groups
Valerii A. Faiziev, Prasanna K. Sahoo
Banach J. Math. Anal. 1(1): 43-55 (2007). DOI: 10.15352/bjma/1240321554


In this paper, we study the stability of the system of functional equations $f(xy)+f(xy^{-1})=2f(x)+f(y)+f(y^{-1})$ and $f(yx)+f(y^{-1}x)=2f(x)+f(y)+f(y^{-1})$ on groups. Here $f$ is a real-valued function that takes values on a group. Among others we proved the following results: 1) the system, in general, is not stable on an arbitrary group; 2) the system is stable on Heisenberg group $UT(3, K)$, where $K$ is a commutative field with characteristic different from two; 3) the system is stable on certain class of $n$-Abelian groups; 4) any group can be embedded into a group where this system is stable.


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Valerii A. Faiziev. Prasanna K. Sahoo. "On the stability of Drygas functional equation on groups." Banach J. Math. Anal. 1 (1) 43 - 55, 2007.


Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1130.39023
MathSciNet: MR2350193
Digital Object Identifier: 10.15352/bjma/1240321554

Primary: 39B52‎
Secondary: 39B72

Keywords: additive character of a group , bihomomorphism , Drygas functional equation , Homomorphism , Jensen functional equation , Metabelian group , n-Abelian group , quadratic functional equation

Rights: Copyright © 2007 Tusi Mathematical Research Group


Vol.1 • No. 1 • 2007
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