On Integral Operators

Let fn z.szr 1yz.nq1, ngNo, and fn y1.be defined such that fn) fn y1. s z , where ) denotes convolution Hadamard product.. Let f be analytic in 1 y z the unit disc E. We define a new operator I fsf y1.n n ) f which is analogous to one defined by Ruscheweyh. Using this operator, the classes M Un. are defined. A function f, analytic in E, is in M Un. if and only if In f is close-to-convex. The properties of fgMU are discussed in some detail. It is shown that MU ;MU n. n. nq1. for ngNo and for ns0, 1, M Un. consists entirely of univalent functions. Closure properties of some integral operators defined on M Un. are also given.