2017
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Quadratic $alpha$functional equations
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In this paper, we solve the quadratic $alpha$functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{2}f(alpha(xy)); (0.1)$ where $alpha$ is a fixed nonArchimedean number with $alpha^{2}neq 3$. Using the fixed point method and the direct method, we prove the HyersUlam stability of the quadratic $alpha$functional equation (0.1) in nonArchimedean Banach spaces.
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Choonkil
Park
Research nstitute for natural sciences,
Hanyang University Seoul 04763,
Korea
Research nstitute for natural sciences,
Hanyang
Iran
baak@hanyang.ac.kr


Sang Og
Kim
Department of Mathematics
Hallym University
Chuncheon 24252
Korea
Department of Mathematics
Hallym University
Chun
Iran
sokim@hallym.ac.kr
HyersUlam stability
nonArchimedean normed space
direct method
fixed point
quadratic $alpha$functional equation