Before revision:  In this paper we consider the problem of sorting unsigned permutations by prefix reversals and prefix transpositions , where a prefix reversal or a prefix transposition is applied always at the unsorted suffix of the given permutation.
After revision:  In this paper we consider the problem of sorting unsigned permutations by prefix reversals and prefix transpositions and present a 3-approximation algorithm for this problem. Then we give a 2-approximation algorithm for sorting by prefix reversals and prefix transreversals. We also provide a 3-approximation algorithm for sorting by prefix reversals and prefix transpositions where the operations are always applied at the unsorted suffix of the given permutation.