## 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.

### MSC:

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

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