- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 1 Issue: 2
- Remarks on solutions to the functional equations of the radical type
Remarks on solutions to the functional equations of the radical type
Authors : Janusz Brzdek
Pages : 125-135
Doi:10.31197/atnaa.379095
View : 3 | Download : 1
Publication Date : 2017-12-20
Article Type : Research
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