Remarks on solutions to the functional equations of the radical type

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Advances in the Theory of Nonlinear Analysis and its Application
Volume: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

Pages : 125-135

View : 7 | Download : 4

Publication Date : 2017-12-20

Article Type : Research Paper

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= finsert ignore into journalissuearticles values(x); + finsert ignore into journalissuearticles values(y);,f n √xn + yn+ fn p|xn −yn|= 2finsert ignore into journalissuearticles values(x); + 2finsert ignore into journalissuearticles values(y); considered recently in several papers, for real functions and with given positive integer n, in connection with the notion of Ulam insert ignore into journalissuearticles values(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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