On a Pexiderized conditional exponential functional equation. (English) Zbl 1212.39039

Let \(f:X\to Y\) be a function where \((X, +)\) is a groupoid and \((Y, \cdot)\) a semigroup, both with neutral elements. The stability of the conditional exponential equation \[ f(x+y)=f(x)f(y)\qquad((x,y)\in D\subset X\times X) \] and its Pexiderized version is studied in a quite general setting. The results include some known theorems concerning orthogonal and some other conditional exponential equations.


39B55 Orthogonal additivity and other conditional functional equations
39B82 Stability, separation, extension, and related topics for functional equations
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