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

Hark-Mahn Kim (), Kil-Woung Jun () and Eunyoung Son ()
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Hark-Mahn Kim: Chungnam National University
Kil-Woung Jun: Chungnam National University
Eunyoung Son: Chungnam National University

A chapter in Handbook of Functional Equations, 2014, pp 243-254 from Springer

Abstract: 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.

Keywords: Cauchy–Jensen type mappings; Hyers–Ulam stability; Homomorphisms; Quasi-β-normed spaces (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1286-5_11

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DOI: 10.1007/978-1-4939-1286-5_11

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