On a singular case in the Hyers–Ulam–Rassias stability of the Wigner equation

Investigating the stability of the Wigner equation where the class of its approximate solutions is defined by the inequality f (x)|f (y) − | x|y | ε x p y p, x,y∈ E (E\ {0} for p<0) (for E,F Hilbert spaces, f : E→F, ε >0, p ∈ R) we notice that the results are different for p = 1. We consider this case and its consequences for a conditional Wigner equation.  2003 Elsevier Inc. All rights reserved.