tailieunhanh - Báo cáo hóa học: " Research Article Some Properties of Certain Class 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 Properties of Certain Class of Integral Operators | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 531540 10 pages doi 2011 531540 Research Article Some Properties of Certain Class of Integral Operators Jian-Rong Zhou 1 Zhi-Hong Liu 2 and Zhi-Gang Wang3 1 Department of Mathematics Foshan University Foshan 528000 Guangdong China 2 Department of Mathematics Honghe University Mengzi 661100 Yunnan China 3 School of Mathematics and Computing Science Changsha University of Science and Technology Yuntang Campus Changsha Hunan 410114 China Correspondence should be addressed to Zhi-Gang Wang zhigangwang@ Received 17 October 2010 Accepted 10 January 2011 Academic Editor Andrea Laforgia Copyright 2011 Jian-Rong Zhou 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. The main object of this paper is to derive some inequality properties and convolution properties of certain class of integral operators defined on the space of meromorphic functions. 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 ỉbkzk 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 1 Xakbkzk g f zi- z k 1 For two functions f and g analytic in U we say that the function f is subordinate to g in U and write f z g z if there exists a Schwarz function w which is analytic in U with w 0 0 Mz 1 z e U such that f z gA A z e U . Indeed it is known that f z g z f 0 g 0 f U c g U . Furthermore if the function g is univalent in U then we have the following equivalence f z g z . f 0 g 0 f U c g U . Analogous to the integral operator .