Korean J. Math.  Vol 24, No 1 (2016)  pp.41-49
DOI: https://doi.org/10.11568/kjm.2016.24.1.41

The Hyers-Ulam stability of a quadratic functional equation with involution in paranormed spaces

Chang Il Kim, Chang Hyeob Shin

Abstract


In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation
\begin{eqnarray*}
& &f(x+y+z)+f(\sigma(x)+y+z)+f(x+\sigma(y)+z)+f(x+y+\sigma(z))\\
&=&4f(x)+4f(y)+4f(z)
\end{eqnarray*}
with involution in paranormed spaces.


Keywords


quadratic functional equation, involution, fixed point method, paranormed space

Subject classification

39B82, 39B52.

Sponsor(s)



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References


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