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

Abstract

Abstract 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 ⊥ y, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces. Mathematics Subject Classification (2010): Primary 39B55, 46S10, 39B72, 39B52, 54E40, 47H10, 47S10, 26E30, 12J25, 46H25.