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 parallel to<f(x)vertical barf(y)>\-\<x\y>\\less than or equal toepsilonparallel toxparallel to(p)parallel toyparallel to(p), x, yis an element ofE (E\{0} for p<0 (for E, F Hilbert spaces, f: E -> F, epsilon>0, p is an element of R) we notice that the results are different for p=1. We consider this case and its consequences for a conditional Wigner equation. (C) 2003 Elsevier Inc. All rights reserved.