@article{article_379095, title={Remarks on solutions to the functional equations of the radical type}, journal={Advances in the Theory of Nonlinear Analysis and its Application}, volume={1}, pages={125–135}, year={2017}, DOI={10.31197/atnaa.379095}, author={Brzdek, Janusz}, keywords={functional equation,radical type,Cauchy equation,quadratic equation}, 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.}, number={2}, publisher={Erdal KARAPINAR}