Stability and superstability of \(*\)- bihomomorphisms on \(C^*\)-ternary algebras (Q2917699)

An equation \(E(f)=0\) is superstable, whenever the boundedness of \(E(f)\) shows that either \(f\) is bounded or \(E(f)=0\). Suppose that \(A\) and \(B\) are \(C^*\)-ternary algebras. A bihomomorphism \(f:A\times A\to B\) is called a \(*\)-homomorphism if \(f(x,y)^*=f(x^*,y^*)\) for each \(x, y \in A\). In this paper the authors investigate the stability and superstability of \(*\)-bihomomorphisms on \(C^*\)-ternary algebras associated with the following functional equation NEWLINE\[NEWLINEf(x-y, t)+f(x, t-s)=2f(x, t)-f(y, t)-f(x, s),NEWLINE\]NEWLINE where \(x, y\in A\) and \(t, s\in B\). There are several typos in the paper.