On a New Stability Problem of Radical nth-Degree Functional Equation by Brzdęk’s Fixed-Point Method

In this paper, we introduce the radical nth-degree functional equation of the form f(xn+ynn)=f(x)+f(y) with a positive integer n, discuss its general solutions, and prove new Hyers-Ulam-type stability results for the equation by using Brzdęk’s fixed-point method.

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Bibliographic Details
Published in:Journal of function spaces 2019-01, Vol.2019 (2019), p.1-6
Main Authors: Kang, Dongseung, Kim, Hoewoon B.
Format: Article
Language:English
Subjects:
Analysis
Banach spaces
Fixed points (mathematics)
Functional equations
Mathematical functions
Methods
Numerical analysis
Stability
Theorems
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Summary:In this paper, we introduce the radical nth-degree functional equation of the form f(xn+ynn)=f(x)+f(y) with a positive integer n, discuss its general solutions, and prove new Hyers-Ulam-type stability results for the equation by using Brzdęk’s fixed-point method.
ISSN:2314-8896
2314-8888
DOI:10.1155/2019/2716107