Open Access

  

Original research article

Remarks on solutions to the functional equations of the radical type

Author(s):

Janusz Brzdęk

Department of Mathematics, Pedagogical University, Kraków, Poland

Advances in the Theory of Nonlinear Analysis and its Applications 1(2), 125-135.
Received: October 15, 2017

  

  

  

Accepted: December 4, 2017

  

Published: December 11, 2017

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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APA Style

Brzdek, J. (2017). Remarks on solutions to the functional equations of the radical type. Advances in the Theory of Nonlinear Analysis and its Application1(2), 125-135.