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Journal of Mathematical Analysis and Applications
Volume 238, Issue 2, 15 October 1999, Pages 341-352
 
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doi:10.1006/jmaa.1999.6501    How to Cite or Link Using DOI (Opens New Window)
Copyright © 1999 Academic Press. All rights reserved.

Regular Article

On Integral Operators*1

Khalida Inayat Noor and Muhammad Aslam Noor

Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5f1

Received 12 April 1999. 
Available online 27 March 2002.

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Abstract

Let fn(z) = z/(1 − z)n + 1, n set membership, variant No, and f(−1)n be defined such that Image , 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 set membership, variant M*(n) are discussed in some detail. It is shown that M*(n) subset of M*(n + 1) for n set membership, variant 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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