Two classes of permutation polynomials over finite fields

Two new classes of permutation polynomials over finite fields are presented: (i) over Fe3 where e is a positive even integer; (ii) over Fpe where e is a positive integer such that if p=2, and n=(p−1)pm+p0e+p1e+⋯+p(p−1)e, (m−1,e)=1. The permutation polynomial in (i) answers an open question about reversed Dickson polynomials.