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On Certain Subclasses of Meromorphically https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq1_HTML.gif -Valent Functions Associated by the Linear Operator https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq2_HTML.gif

Journal of Inequalities and Applications20112011:401913

DOI: 10.1155/2011/401913

Received: 26 July 2010

Accepted: 28 February 2011

Published: 14 March 2011

Abstract

The purpose of this paper is to introduce two novel subclasses https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq3_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq4_HTML.gif of meromorphic https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq5_HTML.gif valent functions by using the linear operator https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq6_HTML.gif . Then we prove the necessary and sufficient conditions for a function https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq7_HTML.gif in order to be in the new classes. Further we study several important properties such as coefficients inequalities, inclusion properties, the growth and distortion theorems, the radii of meromorphically https://static-content.springer.com/image/art%3A10.1155%2F2011%2F401913/MediaObjects/13660_2010_Article_2339_IEq8_HTML.gif valent starlikeness, convexity, and subordination properties. We also prove that the results are sharp for a certain subclass of functions.

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Authors’ Affiliations

(1)
Department of Mathematics, University Putra Malaysia

Copyright

© A. Saif and A. Kılıçman. 2011

This article is published under license to BioMed Central Ltd. 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.