Copyright © 1999 Academic Press. All rights reserved.
Regular Article
On Integral Operators*1
Received 12 April 1999.
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Abstract
Let fn(z) = z/(1 − z)n + 1, n
No, and f(−1)n be defined such that
, where * denotes convolution (Hadamard product). Let f be analytic in the unit disc E. We define a new operator Inf = f(−1)n * 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 Inf is close-to-convex. The properties of f
M*(n) are discussed in some detail. It is shown that M*(n)
M*(n + 1) for n
No 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.
Author Keywords: convolution; Ruscheweyh derivative; close-to-convex; univalent; integral operator.







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