We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which a
A property(C) for permutation pairs is introduced. It is shown that if a pair{π1, π2} of permutations of(1,2,…,n) has property(C),then the D-type map Φπ1,