Banach Journal of Mathematical Analysis

On the stability of Drygas functional equation on groups

Valerii A. Faiziev and Prasanna K. Sahoo

Full-text: Open access

Abstract

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.

Article information

Source
Banach J. Math. Anal., Volume 1, Number 1 (2007), 43-55.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240321554

Digital Object Identifier
doi:10.15352/bjma/1240321554

Mathematical Reviews number (MathSciNet)
MR2350193

Zentralblatt MATH identifier
1130.39023

Subjects
Primary: 39B52: Equations for functions with more general domains and/or ranges
Secondary: 39B72: Systems of functional equations and inequalities

Keywords
additive character of a group bihomomorphism Drygas functional equation homomorphism Jensen functional equation metabelian group n-Abelian group quadratic functional equation

Citation

Faiziev, Valerii A.; Sahoo, Prasanna K. On the stability of Drygas functional equation on groups. Banach J. Math. Anal. 1 (2007), no. 1, 43--55. doi:10.15352/bjma/1240321554. https://projecteuclid.org/euclid.bjma/1240321554


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