Remarks on solutions to the functional equations of the radical type

Year 2017, Volume: 1 Issue: 2, 125 - 135, 20.12.2017

Janusz Brzdek

https://doi.org/10.31197/atnaa.379095

Cited By: 1

Abstract

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.

Keywords

functional equation, radical type, Cauchy equation, quadratic equation

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