Results of a perturbation theory generating a one-parameter semigroup

This paper consists of the results about ω -order preserving partial contraction mapping using perturbation theory to generate a one-parameter semigroup. We show that adding a bounded linear operator B to an infinitesimal generator A of a semigroup of the linear operator does not destroy A’s property. Furthermore, A is the generator of a one-parameter semigroup, and B is a small perturbation so that A + B is also the generator of a one-parameter semigroup.