On the stability of functional equations with square-symmetric operation (Q2720287)

The author studies the stability (in the sense of Hyers-Ulam) of the family of functional equations of the form NEWLINE\[NEWLINE f(x\circ y)=H(f(x),f(y)), NEWLINE\]NEWLINE 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., NEWLINE\[NEWLINE H(uv,uw)=uH(v,w), \quad u,v,w \in G .NEWLINE\]