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vResearch Article Coefficient Bounds for Certain Classes of Meromorphic Functions"

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 Coefficient Bounds for Certain Classes of Meromorphic Functions | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 931981 9 pages doi 10.1155 2008 931981 Research Article Coefficient Bounds for Certain Classes of Meromorphic Functions H. Silverman 1 K. Suchithra 2 B. Adolf Stephen 3 and A. Gangadharan2 1 Department of Mathematics College of Charleston Charleston SC 29424 USA 2 Department of Applied Mathematics Sri Venkateswara College of Engineering Sriperumbudur Chennai 602105 Tamilnadu India 3 School of Mathematical Sciences Universiti Sains Malaysia 11800 Penang Malaysia Correspondence should be addressed to H. Silverman silvermanh@cofc.edu Received 19 May 2008 Revised 9 September 2008 Accepted 4 December 2008 Recommended by Ramm Mohapatra Sharp bounds for a1 - pa2 are derived for certain classes and satf of meromor-phic functions f z defined on the punctured open unit disk for which -zf z f z and - 1 - 2a zf z az2f z 1 - a f z - azffz a e C - 0 1 R a 0 respectively lie in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain applications of the main results for a class of functions defined through Ruscheweyh derivatives are obtained. Copyright 2008 H. Silverman 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 s denote the class of functions of the form f z 1 y akzk z k 0 which are analytic and univalent in the punctured open unit disk A z e C 0 z 1 A - 0 1.1 1.2 where A is the open unit disk A z e C z 1 . A function f e s is said to be meromorphic univalent starlike of order a if -R zf V f z z e A 0 a 1 1.3 a 2 Journal of Inequalities and Applications and the class of all such meromorphic univalent starlike functions in A is denoted by s a . Recently Uralegaddi and Desai 1 studied the class s a fi of functions f e s satisfying the condition zf z f z 1 zf z