Janusz Brzdęk
Department of Mathematics, Pedagogical University, Kraków, Poland
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.
Brzdek, J. (2017). Remarks on solutions to the functional equations of the radical type. Advances in the Theory of Nonlinear Analysis and its Application, 1(2), 125-135.