The authors prove the orthogonal stability of the quadratic functional equation of Pexider type by using the fixed point alternative theorem. The following theorem is the main result of this paper: Suppose that is a real orthogonality space with a symmetric orthogonal relation and is a Banach space. Let the mappings satisfy
for all with . There exist an orthogonally additive mapping and a constant such that
if and only if there exists a constant with
Indeed, if satisfies
then there exist orthogonally additive mappings such that
for all .
In the Introduction, quoting the stability of quadratic equations of Pexider type, the authors missed citing a paper “Stability of the quadratic equation of Pexider type” [Abh. Math. Semin. Univ. Hamb. 70, 175–190 (2000; Zbl 0991.39018)] by S.-M. Jung, which contains the first result about the stability of quadratic equations of Pexider type (see Theorem 5 and Corollary 6 in the paper).