Let R be a Riemann surface and X be any nonempty subset of R. E(R,X) denotes the semigroup, under composition, of ali holomorphic selfmaps of R which carry X into X and is referred to as a restrictive semigroup of holomorphic endomorphisms. Let R , R2 be Riemann surfaces which have bounded nonconstant holomorphic fiınctions and X, Y be any subsets of Rp R2> respectively. If