On a functional equation of Bruce Ebanks

被引：3
作者：
Brillouet-Belluot, Nicole [1 ]
机构：
[1] Ecole Cent Nantes, Dept Math & Informat, F-44321 Nantes 3, France
来源：
AEQUATIONES MATHEMATICAE | 2014年 / 87卷 / 1-2期
关键词：
Functional equation; continuous solution; cancellative associative operation; Cauchy's equation;
D O I：
10.1007/s00010-013-0209-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper Brillouet-Belluot and Ebanks (Aequationes Math 60:233-242, 2000), the authors found all continuous functions f: [0, 1] -> [0, + infinity) which verify f(0) = f(1) = 0 and the functional equation f (xy + cf (x) f (y)) = xf (y) + yf(x) + d f(x)f(y) (1) where c and d are given real numbers with c not equal 0. In the present paper we obtain all continuous solutions f : R -> R of the functional equation (1).
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页码：173 / 189
页数：17
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