摘要：In this paper, we investigate the orthogonal stability of functional equations in orthogonality modules over a unital Banach algebra. Using a fixed point method, we prove the Hyers-Ulam stability of the orthogonally Jensen additive functional equation 2 f ( x + y 2 ) = f ( x ) + f ( y ) , the orthogonally Jensen quadratic functional equation 2 f ( x + y 2 ) + 2 f ( x − y 2 ) = f ( x ) + f ( y ) , the orthogonally cubic functional equation f ( 2 x + y ) + f ( 2 x − y ) = 2 f ( x + y ) + 2 f ( x − y ) + 12 f ( x ) , and the orthogonally quartic functional equation f ( 2 x + y ) + f ( 2 x − y ) = 4 f ( x + y ) + 4 f ( x − y ) + 24 f ( x ) − 6 f ( y ) for all x, y with x ⊥ y , where ⊥ is the orthogonality in the sense of Rätz. MSC:39B55, 47H10, 39B52, 46H25.
关键词：Hyers-Ulam stability ; orthogonally (Jensen additive, Jensen quadratic, cubic, quartic) functional equation ; fixed point ; orthogonality module over Banach algebra ; orthogonality space
