Annals of Functional Analysis

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

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

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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 $x,y,u,v\in\Bbb{R}$, where $f:\Bbb{R}^{2}\to\Bbb{R}$, which arise from number theory and are connected with the characterizations of the determinant and permanent of two-by-two matrices.

Article information

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

Received: 8 July 2016
Accepted: 21 October 2016
First available in Project Euclid: 4 April 2017

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Digital Object Identifier

Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 39B52: Equations for functions with more general domains and/or ranges

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


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.

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