tailieunhanh - Báo cáo hóa học: " Research Article Some Subclasses of Meromorphic Functions Associated with a Family of Integral Operators"

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 Some Subclasses of Meromorphic Functions Associated with a Family of Integral Operators | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 931230 18 pages doi 2009 931230 Research Article Some Subclasses of Meromorphic Functions Associated with a Family of Integral Operators Zhi-Gang Wang 1 Zhi-Hong Liu 2 and Yong Sun3 1 School of Mathematics and Computing Science Changsha University of Science and Technology Yuntang Campus Changsha Hunan 410114 China 2 School of Mathematics Honghe University Mengzi Yunnan 661100 China 3 Department of Mathematics Huaihua University Huaihua Hunan 418008 China Correspondence should be addressed to Zhi-Gang Wang zhigangwang@ Received 11 July 2009 Accepted 3 September 2009 Recommended by Narendra Kumar Govil Making use of the principle of subordination between analytic functions and a family of integral operators defined on the space of meromorphic functions we introduce and investigate some new subclasses of meromorphic functions. Such results as inclusion relationships and integralpreserving properties associated with these subclasses are proved. Several subordination and superordination results involving this family of integral operators are also derived. Copyright 2009 Zhi-Gang Wang 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 and Preliminaries Let s denote the class of functions of the form f z 1 ỉakzk z k 1 which are analytic in the punctured open unit disk U z z e C 0 z 1 U 0 . Let f g e s where f is given by and g is defined by g z 1 2 bkZk. z k 1 2 Journal of Inequalities and Applications Then the Hadamard product or convolution f g of the functions f and g is defined by f g z I Ukbkzk g f z . z k 1 Let P denote the class of functions of the form TO p z 1 Pkz k 1 which are analytic and convex in U and satisfy the condition R p z 0 z e U .