Annals of Functional Analysis

Stability of a functional equation coming from the characterization of the absolute value of additive functions

Attila Gilányi, Kaori Nagatou, and Peter Volkmann

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Abstract

‎In the present paper‎, ‎we prove the stability of the functional equation‎ ‎\[‎ ‎\max\{f((x\circ y)\circ y),f(x)\}=f(x\circ y)+f(y)‎ ‎\]‎ ‎for real valued functions defined on a square-symmetric groupoid‎ ‎with a left unit element‎. ‎As a consequence‎, ‎we obtain the known result about the stability of the equation‎ ‎\[‎ ‎\max\{f(x+y),f(x-y)\}=f(x)+f(y)‎ ‎\]‎ ‎for real valued functions defined on an abelian group‎.

Article information

Source
Ann. Funct. Anal., Volume 1, Number 2 (2010), 1- 6.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900582

Digital Object Identifier
doi:10.15352/afa/1399900582

Mathematical Reviews number (MathSciNet)
MR2772033

Zentralblatt MATH identifier
1219.39014

Subjects
Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 39B52‎ ‎46E99

Keywords
Stability of functional equations ‎square-symmetric groupoids

Citation

Gilányi, Attila; Nagatou, Kaori; Volkmann, Peter. Stability of a functional equation coming from the characterization of the absolute value of additive functions. Ann. Funct. Anal. 1 (2010), no. 2, 1-- 6. doi:10.15352/afa/1399900582. https://projecteuclid.org/euclid.afa/1399900582


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