A note on functional equations connected with the Cauchy mean value theorem

被引：1
|
作者：
Lukasik, Radoslaw [1 ]
机构：
[1] Univ Silesia, Inst Math, Ul Bankowa 14, PL-40007 Katowice, Poland
来源：
AEQUATIONES MATHEMATICAE | 2018年 / 92卷 / 05期
关键词：
Functional equation; Mean value theorem; Linearly dependent functions; QUADRATIC POLYNOMIALS; PROPERTY;
D O I：
10.1007/s00010-018-0583-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to describe the solution (f, g) of the equation [f(x) - f(y)]g' (alpha x + (1 - alpha)y) = [g(x) - g(y)]f'(alpha x + (1 - alpha)y), x, y is an element of I, where I subset of R is an open interval, f, g : I -> R are differentiable, alpha is a fixed number from (0, 1).
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页码：935 / 947
页数：13
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