Korean J. Math. Vol. 20 No. 1 (2012) pp.77-89
DOI: https://doi.org/10.11568/kjm.2012.20.1.077

FUNCTIONAL EQUATIONS IN ORTHOGONALITY SPACES

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Choonkil Park

Abstract

Using fixed point method, we prove the Hyers-Ulam
stability of the orthogonally additive functional equation
f(2x+y)=2f(x)+f(y)
and of the orthogonally quadratic functional equation
2f(x2+y)+2f(x2y)=f(x)+4f(y)

for all x, y with x ⊥ y in orthogonality spaces.



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