TY  - JOUR
T1  - Remarks on solutions to the functional equations of the radical type
AU  - Brzdek, Janusz
PY  - 2017
DA  - December
DO  - 10.31197/atnaa.379095
JF  - Advances in the Theory of Nonlinear Analysis and its Application
JO  - ATNAA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2587-2648
SP  - 125
EP  - 135
VL  - 1
IS  - 2
LA  - en
AB  - 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.
KW  - functional equation
KW  - radical type
KW  - Cauchy equation
KW  - quadratic equation
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UR  - https://doi.org/10.31197/atnaa.379095
L1  - https://dergipark.org.tr/en/download/article-file/596296
ER  -