Stability of two functional equations arising from number theory

被引：0

作者：

Chung, Jaeyoung ^{[1
]}

Chang, Jeongwook ^{[2
]}

Choi, Chang-Kwon ^{[3
]}

机构：

[1] Kunsan Natl Univ, Dept Math, Kunsan 573701, South Korea

[2] Dankook Univ, Dept Math Educ, Yongin 448701, South Korea

[3] Jeonbuk Natl Univ, Dept Math, Jeonju 561756, South Korea

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2015年 / 26卷 / 01期

关键词：

Exponential functional equation; Multiplicative function; Quaternion; Stability;

D O I：

10.1016/j.indag.2014.09.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Generalizing two functional equations introduced in Houston and Sahoo (2008), Jung and Bae (2003), which arise from number theory we prove the stability of the equations f(x(1)x(2) + y(1)y(2), x(1)y(2) - x(2)y(1)) = g(x(1), y(1))h(x(2), y(2)) for all x(1), y(1), x(2), y(2) is an element of R, where f, g, h : R-2 -> R, and g(x(1), y(1), u(1), v(1))h(x(2), y(2), u(2), v(2)) = f(x(1)x(2) + y(1)y(2) + u(1)u(2) + v(1)v(2), x(1)y(2) - y(1)x(2) + u(1)v(2) - v(1)u(2,,) x(1)u(2) - y(1)v(2) - u(1)x(2) + v(1)y(2), x(1)v(2) + y(1)u(2) - u(1)y(2) - v(1)x(2)) for all x(1,) x(2,) y(1,) y(2,) u(1,) u(2,) v(1.) v(2) is an element of R, where f, g, h : R-4 -> R. (C) 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：206 / 218

页数：13