Orthogonally additive-additive and orthogonally quadratic-quadratic functional equation in orthogonality spaces

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-additive and orthogonally quadratic-quadratic functional equation f(x+y+z/2) + f(x+y-z/2) + f(x-y+z/2) + f(y+z-x/2) = f(x) + f(y) + f(z) for all x, y, z with x aSyen y, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2012R1A1A2004299). D. Y. Shin was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2010-0021792)