General solutions of two quadratic functional equations of Pexider type on orthogonal vectors. (English) Zbl 1246.39023

Fochi, Margherita

Abstr. Appl. Anal. 2012, Article ID 675810, 10 p. (2012).

Summary: Based on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this paper we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, and the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.

MSC:

39B82

Stability, separation, extension, and related topics for functional equations

Keywords:

Hyers-Ulam stability; orthogonal stability; Pexider-quadratic functional equations

References:

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