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Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type f (x + y) + g(x − y) = h(x) + k(y), where f, g, h, k are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on f . 2000 Mathematics Subject Classification. Primary 39B55; Secondary 39B52; 39B82.

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Abstract. Let A be a C * -algebra acting on a Hilbert space H, let σ : A → B(H) be a linear mapping and let d : A → B(H) be a σ-derivation. Generalizing the celebrated theorem of Sakai, we prove that if σ is a continuous * -mapping, then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous * -σ-derivation, then there exists a continuous linear mapping Σ :The continuity of the so-called * -(σ, τ )-derivations is also discussed.