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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
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