tailieunhanh - Báo cáo hóa học: " Research Article The Radius of Starlikeness of the Certain Classes of p-Valent Functions Defined by "

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 The Radius of Starlikeness of the Certain Classes of p-Valent Functions Defined by | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 280183 5 pages doi 2008 280183 Research Article The Radius of Starlikeness of the Certain Classes of p-Valent Functions Defined by Multiplier Transformations Mugur Acu 1 Yasar Polatoglu 2 and Emel Yavuz2 1 Department of Mathematics Lucian Blaga University ofSibiu 5-7 Ion Ratiu Street Sibiu 550012 Romania 2 Department of Mathematics and Computer Science TC Istanbul Kultur University Istanbul 34156 Turkey Correspondence should be addressed to Emel Yavuz Received 12 November 2007 Accepted 02 January 2008 Recommended by Narendra Kumar K. Govil The aim of this paper is to give the radius of starlikeness of the certain classes of p-valent functions defined by multiplier transformations. The results are obtained by using techniques of Robertson 1953 1963 which was used by Bernardi 1970 Libera 1971 Livingstone 1966 and Goel 1972 . Copyright 2008 Mugur Acu 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 class of analytic functions in the open unit disc D z G C z 1 and H a n be the subclasses of H consisting of the functions of the form f z a anzn an 1zn 1 . Let A p n denote the class of functions f z normalized by rc f z zp ỵ akzk p n G N 1 2 3 . k n p which are analytic in the open unit disc D. In particular we set A p 1 Ap A 1 1 A A1. If f z and g z are analytic in D we say that f z is subordinate to g z written symbolically as f g or f z g z z G D . 2 Journal of Inequalities and Applications If there exists a Schwarz function wfiz which is analytic in D with w 0 0 w z 1 such that f z g w z z D. For two analytic functions f z and F z we say that F z is superordinate to f z if f z is subordinate to F z . For integer n 1 let Q n denote the class .