Solution of Several Functional Equations on Nonunital Semigroups Using Wilson's Functional Equations with Involution

被引：5

作者：

Chung, Jaeyoung ^{[1
]}

Sahoo, Prasanna K. ^{[2
]}

机构：

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

[2] Univ Louisville, Dept Math, Louisville, KY 40292 USA

来源：

ABSTRACT AND APPLIED ANALYSIS | 2014年

基金：

新加坡国家研究基金会;

关键词：

DALEMBERTS;

D O I：

10.1155/2014/463918

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let S be a nonunital commutative semigroup, sigma : S -> S an involution, and C the set of complex numbers. In this paper, first we determine the general solutions f, g : S -> C of Wilson's generalizations of d'Alembert's functional equations f(x + y) + f(x + sigma y) = 2 f(x)g(y) and f(x + y) + f(x + sigma y) = 2g(x)f(y) on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains.

引用

页数：9

共 22 条

[1]

Aczel J., 1989, ENCY MATH APPL, V31

[2]

Aczel J, 2006, Lectures on Functional Equations and their Applications

[3] On solutions of the second generalization of d'Alembert's functional equation on a restricted domain [J].