tailieunhanh - Báo cáo hóa học: " Research Article Subordination and Superordination for Multivalent Functions Associated with the Dziok-Srivastava Operator"

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 Subordination and Superordination for Multivalent Functions Associated with the Dziok-Srivastava Operator | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 486595 17 pages doi 2011 486595 Research Article Subordination and Superordination for Multivalent Functions Associated with the Dziok-Srivastava Operator Nak Eun Cho 1 Oh Sang Kwon 2 Rosihan M. Ali 3 and V. Ravichandran3 4 1 Department of Applied Mathematics Pukyong National University Busan 608-737 Republic of Korea 2 Department of Mathematics Kyungsung University Busan 608-736 Republic of Korea 3 School of Mathematical Sciences Universiti Sains Malaysia 11800 Penang Malaysia 4 Department of Mathematics University of Delhi Delhi 110007 India Correspondence should be addressed to Rosihan M. Ali rosihan@ Received 21 September 2010 Revised 18 January 2011 Accepted 26 January 2011 Academic Editor P. J. Y. Wong Copyright 2011 Nak Eun Cho 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. Subordination and superordination preserving properties for multivalent functions in the open unit disk associated with the Dziok-Srivastava operator are derived. Sandwich-type theorems for these multivalent functions are also obtained. 1. Introduction Let u z e c z 1 be the open unit disk in the complex plane c and let H H U denote the class of analytic functions defined in u. For n e N 1 2 . and a e c let H a n consist of functions f e H of the form f z a anzn an 1 zn 1 . Let f and F be members of H. The function f is said to be subordinate to F or F is said to be superordinate to f if there exists a function w analytic in u with w z z and such that f z F w z . In such a case we write f F or f z F z . If the function F is univalent in u then f F if and only if f 0 F 0 and f U c F U cf. 1 2 . Let y c2 c and let h be univalent in u. The subordination y p z zpfzf hfz is called a first-order differential .

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