tailieunhanh - Báo cáo hóa học: " Research Article Double Subordination-Preserving Properties for Certain 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 Double Subordination-Preserving Properties for Certain Integral Operators | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 83073 10 pages doi 2007 83073 Research Article Double Subordination-Preserving Properties for Certain Integral Operators Nak Eun Cho and Shigeyoshi Owa Received 27 November 2006 Revised 3 January 2007 Accepted 4 January 2007 Recommended by Narendra K. Govil The purpose of the present paper is to obtain the sandwich-type theorem which contains the subordination- and superordination-preserving properties for certain integral operators defined on the space of normalized analytic functions in the open unit disk. Copyright 2007 N. E. Cho and S. Owa. 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 X U denote the class of analytic functions in the open unit disk U z e C Izl 1 . For a e C let a n f e X f z a anzn an 1zn 1 . Let f and F be members of X. 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 0 0 and w z 1 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 ộ C2 C and let h be univalent in U. If p is analytic in U and satisfies the differential subordination ộ p z zp z h z z e U then p is called a solution of the differential subordination. The univalent function q is called a dominant of the solutions of the differential subordination or more simply a dominant if p q for all p satisfying . A dominant q that satisfies q q for all dominants q of is said to be the best dominant 1 . 2 Journal of Inequalities and Applications Let p C2 C and let h be analytic in U. If p and ọ p z zp z are univalent in U and satisfy the differential superordination h z ọ p z zp z z e U then p is