On superstability of the Wigner equation

For f:M→N, where M, N are finite or infinite dimensional inner product spaces or Hilbert C⁎-modules over compact operators, we investigate the superstability of the Wigner equation, where the class of its approximate solutions is defined by the inequality||〈f(x),f(y)〉|−|〈x,y〉||≤φ(x,y),x,y∈M.