On integral operators

Let f(n)(z) = z/(1 - z)(n + 1), n is an element of N-o, and f(n)((-1)) be defined such that f(n) * f(n)((-1)) = z/1 - z, where * denotes convolution (Hadamard product). Let f be analytic in the unit disc E. We define a new operator I(n)f = f(n)((-1)) * f which is analogous to one defined by Ruscheweyh. Using this operator, the classes M-(n)* are defined. A function f, analytic in E, is in M-(n)* if and only if I(n)f is close-to-convex. The properties of f is an element of M-(n)* are discussed in some detail. It is shown that M-(n)* subset of M-(n +1)(*) for n is an element of N-o and for n = 0, 1, M-(n)* consists entirely of univalent functions. Closure properties of some integral operators defined on M-(n)* are also given. (C) 1999 Academic Press.