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On Some Functional Equations Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Approximate Cauchy–Jensen Type Mappings in Quasi-β-Normed Spaces

Authors : Hark-Mahn Kim, Kil-Woung Jun, Eunyoung Son

Published in: Handbook of Functional Equations

Publisher: Springer New York

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Abstract

In this chapter, we find the general solution of the following Cauchy–Jensen type functional equation
$$f(\frac{x+y}{n}+z)+f(\frac{y+z}{n}+x)+f(\frac{z+x}{n}+y)=\frac{n+2}{n}[f(x)+f(y)+f(z)],$$
and then investigate the generalized Hyers–Ulam stability of the equation in quasi-β-normed spaces for any fixed nonzero integer n.

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previous chapter Some Functional Equations Related to the Characterizations of Information Measures and Their Stability
next chapter An AQCQ-Functional Equation in Matrix Paranormed Spaces
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Metadata
Title
Approximate Cauchy–Jensen Type Mappings in Quasi-β-Normed Spaces
Authors
Hark-Mahn Kim
Kil-Woung Jun
Eunyoung Son
Copyright Year
2014
Publisher
Springer New York
Book
Handbook of Functional Equations

Print ISBN: 978-1-4939-1285-8

Electronic ISBN: 978-1-4939-1286-5

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4939-1286-5_11

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