Generalized Cauchy difference equations. II

被引：20

作者：

Ebanks, Bruce ^{[1
]}

机构：

[1] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 11期

关键词：

Cauchy difference; cocycle equation; functional independence; Pexider equation; implicit function theorem; philandering; regularity properties; functional equations;

D O I：

10.1090/S0002-9939-08-09379-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main result is an improvement of previous results on the equation f(x) + f(y) - f(x + y) = g[phi f(x) + phi(y) - phi(x + y)] for a given function phi. We find its general solution assuming only continuous differentiability and local nonlinearity of phi. We also provide new results about the more general equation f(x) + f(y) - f(x + y) = g(H(x, y)) for a given function H. Previous uniqueness results required strong regularity assumptions on a particular solution f0, g0. Here we weaken the assumptions on f0, g0 considerably and find all solutions under slightly stronger regularity assumptions on H.

引用

页码：3911 / 3919

页数：9