LOEWNER CHAINS AND UNIVALENCE CRITERIA RELATED WITH RUSCHEWEYH AND SĂLĂGEAN DERIVATIVES

In this paper we obtain, by the method of Loewner chains, some sufficient conditions for the analyticity and the univalence of the functions defined by an integral operator. These conditions involves Ruscheweyh and Salagean derivative operator in the open unit disk. In particular cases, we find the well-known conditions for univalency established by Becker [3], Ahlfors [2], Kanas and Srivastava [8] and others for analytic mappings  f : U ! C: Also,we obtain the corresponding new, useful and simpler conditions for this integral operator.