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
收藏
页码：935 / 947
页数：13
相关论文
共 50 条
  • [11] On means generated through the Cauchy mean value theorem
    Berrone L.R.
    Moro J.
    Aequationes mathematicae, 2000, 60 (1-2) : 1 - 14
  • [12] Cauchy Mean Theorem
    Grabowski, Adam
    FORMALIZED MATHEMATICS, 2014, 22 (02): : 157 - 166
  • [13] A MEAN VALUE THEOREM FOR THE CHEBYSHEV FUNCTIONAL
    Gavrea, Bogdan
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2015, 18 (02): : 751 - 757
  • [14] On the intermediate point in Cauchy's mean-value theorem
    Duca, Dorel I.
    Pop, Ovidiu
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2006, 9 (03): : 375 - 389
  • [15] On Multivariate Fractional Taylor's and Cauchy' Mean Value Theorem
    Cheng, Jinfa
    JOURNAL OF MATHEMATICAL STUDY, 2019, 52 (01): : 38 - 52
  • [16] A note on the mean value theorem for special homogeneous spaces
    Morishita, M
    Watanabe, T
    NAGOYA MATHEMATICAL JOURNAL, 1996, 143 : 111 - 117
  • [17] A note on an approximate mean value theorem for Frechet subgradients
    Nguyen Thi Quynh Trang
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (01) : 380 - 383
  • [18] A Proof of Bonnet's Version of the Mean Value Theorem by Methods of Cauchy
    Plante, Joseph
    AMERICAN MATHEMATICAL MONTHLY, 2017, 124 (03): : 269 - 273
  • [19] Exploring students' proof comprehension of the Cauchy Generalized Mean Value Theorem
    Kolahdouz, Fahimeh
    Radmehr, Farzad
    Alamolhodaei, Hassan
    TEACHING MATHEMATICS AND ITS APPLICATIONS, 2020, 39 (03): : 213 - 235
  • [20] A physically motivated further note on the mean value theorem for integrals
    Schwind, WJ
    Ji, J
    Koditschek, DE
    AMERICAN MATHEMATICAL MONTHLY, 1999, 106 (06): : 559 - 564
12345