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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 820696, 10 pages
http://dx.doi.org/10.1155/2012/820696
Research Article

A Note on the Class of Functions with Bounded Turning

1Institute of Mathematical Sciences, University Malaya, 50603 Kuala Lumpur, Malaysia
2Department of Mathematics, University of Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 1 December 2011; Revised 25 January 2012; Accepted 29 January 2012

Academic Editor: M. Victoria Otero-Espinar

Copyright © 2012 Rabha W. Ibrahim and Adem Kılıçman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider subclasses of functions with bounded turning for normalized analytic functions in the unit disk. The geometric representation is introduced, some subordination relations are suggested, and the upper bound of the pre-Schwarzian norm for these functions is computed. Moreover, by employing Jack's lemma, we obtain a convex class in the class of functions of bounded turning and relations with other classes are posed.