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On the stability of the orthogonal Pexiderized Cauchy equation

Mohammad Sal Moslehian
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Abstract

We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers--Ulam stability of the orthogonal Cauchy functional equation of Pexider type $f_1(x+y)=f_2(x)+f_3(y)$, $x\perp y$ in which $\perp$ is the orthogonality in the sense of Ratz.

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Mohammad Sal Moslehian. 2004-12-23. On the stability of the orthogonal Pexiderized Cauchy equation. https://doi.org/10.1016/j.jmaa.2005.05.052

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