## Annals of Functional Analysis

- Ann. Funct. Anal.
- Volume 8, Number 3 (2017), 329-340.

### Stability of functional equations arising from number theory and determinant of matrices

Chang-Kwon Choi, Jaeyoung Chung, Thomas Riedel, and Prasanna K. Sahoo

#### Abstract

In this paper, we consider the Ulam–Hyers stability of the functional equations $$f(ux-vy,uy-vx)=f(x,y)f(u,v),$$ $$f(ux+vy,uy-vx)=f(x,y)f(u,v),$$ $$f(ux+vy,uy+vx)=f(x,y)f(u,v),$$ $$f(ux-vy,uy+vx)=f(x,y)f(u,v)$$ for all $x,y,u,v\in \mathbb{R}$, where $f:{\mathbb{R}}^{2}\to \mathbb{R}$, which arise from number theory and are connected with the characterizations of the determinant and permanent of two-by-two matrices.

#### Article information

**Source**

Ann. Funct. Anal., Volume 8, Number 3 (2017), 329-340.

**Dates**

Received: 8 July 2016

Accepted: 21 October 2016

First available in Project Euclid: 4 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1491280441

**Digital Object Identifier**

doi:10.1215/20088752-0000017X

**Mathematical Reviews number (MathSciNet)**

MR3689996

**Zentralblatt MATH identifier**

1369.39028

**Subjects**

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

Secondary: 39B52: Equations for functions with more general domains and/or ranges

**Keywords**

bounded solution general solution exponential functional equation multiplicative functional equation number theory Ulam–Hyers stability

#### Citation

Choi, Chang-Kwon; Chung, Jaeyoung; Riedel, Thomas; Sahoo, Prasanna K. Stability of functional equations arising from number theory and determinant of matrices. Ann. Funct. Anal. 8 (2017), no. 3, 329--340. doi:10.1215/20088752-0000017X. https://projecteuclid.org/euclid.afa/1491280441