Stability of functional equations arising from number theory and determinant of matrices. (English) Zbl 1369.39028

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

Ann. Funct. Anal. 8, No. 3, 329-340 (2017).

Summary: In this paper, we consider the Ulam-Hyers stability of the functional equations \[ \begin{aligned} &f(ux-vy,uy-vx)=f(x,y)f(u,v),\\ &f(ux+vy,uy-vx)=f(x,y)f(u,v),\\ &f(ux+vy,uy+vx)=f(x,y)f(u,v),\\ &f(ux-vy,uy+vx)=f(x,y)f(u,v)\end{aligned} \] 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.

MSC:

39B82	Stability, separation, extension, and related topics for functional equations
39B52	Functional equations for functions with more general domains and/or ranges
15A15	Determinants, permanents, traces, other special matrix functions
11C20	Matrices, determinants in number theory

Keywords:

bounded solution; general solution; exponential functional equation; multiplicative functional equation; number theory; Ulam-Hyers stability; determinant; permanent