Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Subclasses of Meromorphic Functions Associated with Convolution | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 190291 9 pages doi 2009 190291 Research Article Subclasses of Meromorphic Functions Associated with Convolution Maisarah Haji Mohd 1 Rosihan M. Ali 1 Lee See Keong 1 and V. Ravichandran2 1 School of Mathematical Sciences Universiti Sains Malaysia 11800 USM Penang Malaysia 2 Department of Mathematics University of Delhi Delhi 110 007 India Correspondence should be addressed to Lee See Keong sklee@ Received 12 December 2008 Accepted 11 March 2009 Recommended by Narendra Kumar Govil Several subclasses of meromorphic functions in the unit disk are introduced by means of convolution with a given fixed meromorphic function. Subjecting each convoluted-derived function in the class to be subordinated to a given normalized convex function with positive real part these subclasses extend the classical subclasses of meromorphic starlikeness convexity close-to-convexity and quasi-convexity. Class relations as well as inclusion and convolution properties of these subclasses are investigated. Copyright 2009 Maisarah Haji Mohd 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. 1. Introduction Let H be the set of all analytic functions defined in the unit disk U z z 1 . We denote by A the class of normalized analytic functions f z z 2 anzn defined in U. For two functions f and g analytic in U the function f is subordinate to g written as f z k g z if there exists a Schwarz function w analytic in U with w 0 0 and w z 1 such that f z g w z Y In particular if the function g is univalent in U then f z k g z is equivalent to f 0 g 0 and f U c g U . A function f eA is starlike if zf z f z is subordinate to 1 z 1 -z and convex if 1 zf z f z is subordinate to 1 z 1-z . Ma and Minda 1 gave a unified presentation
