Remarks on solutions to the functional equations of the radical type

Advances in the Theory of Nonlinear Analysis and its Applications

Janusz Brzdęk¹ 

[1] Department of Mathematics, Pedagogical University, Kraków, Poland.;

关键词: functional equation;    radical type;    Cauchy equation;    quadratic equation;   

DOI  :  10.31197/atnaa.379095

来源: DOAJ

【 摘 要 】

This is an expository paper containing remarks on solutions to some functional equations of a form, that could be called of the radical type. Simple natural examples of them are the following two functional equations fn √xn + yn= f(x) + f(y),f n √xn + yn+ fn p|xn −yn|= 2f(x) + 2f(y) considered recently in several papers, for real functions and with given positive integer n, in connection with the notion of Ulam (or Hyers-Ulam) stability. We provide a general method allowing to determine solutions to them.

【 授权许可】

Unknown