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).

引用

页码：935 / 947

页数：13

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