  Let $\mathbb{F}_q$ denote the finite fields with $q$ elements. The
permutation behavior of several classes of infinite families of permutation
polynomials over finite fields have been studied in recent years. In this
paper, we continue with their studies, and get some further results about the
permutation properties of the permutation polynomials. Also, some new classes
of permutation polynomials are constructed. For these, we alter the
coefficients, exponents or the underlying fields, etc.
