## On the stability of functional equations with square-symmetric operation.(English)Zbl 0990.39028

The author studies the stability (in the sense of Hyers-Ulam) of the family of functional equations of the form $f(x\circ y)=H(f(x),f(y)),$ where $$x,y \in S$$, $$\circ:S \times S \to S$$ is a square-symmetric operation, $$H:G\times G \to G$$, $$G$$ is a closed multiplicative subsemigroup of $$\mathbb C$$ and $$H$$ is $$G$$-homogeneous, i.e., $H(uv,uw)=uH(v,w), \quad u,v,w \in G .$
Reviewer: G.L.Forti (Milano)

### MSC:

 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges

### Keywords:

Hyers-Ulam stability; semigroup; functional equations
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