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Journal of Function Spaces
Volume 2017 (2017), Article ID 9010964, 7 pages
https://doi.org/10.1155/2017/9010964
Research Article

A Subclass of Analytic Functions Related to -Uniformly Convex and Starlike Functions

1Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
2Department of Mathematics & Statistics, Riphah International University, Islamabad, Pakistan
3School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Correspondence should be addressed to Saqib Hussain; moc.oohay@htam_biqas

Received 26 January 2017; Accepted 20 April 2017; Published 23 May 2017

Academic Editor: Maria Alessandra Ragusa

Copyright © 2017 Saqib Hussain et al. 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 investigate some subclasses of -uniformly convex and -uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.