TAILIEUCHUNG - Báo cáo hóa học: " Research Article Certain Integral Operators on the Classes M βi and N βi"

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 Certain Integral Operators on the Classes M βi and N βi | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 719354 4 pages doi 2008 719354 Research Article Certain Integral Operators on the Classes M . and N fi Daniel Breaz Department of Mathematics 1st December 1918 University of Alba Iulia 510009 Alba Romania Correspondence should be addressed to Daniel Breaz dbreaz@ Received 13 September 2007 Revised 21 October 2007 Accepted 2 January 2008 Recommended by Vijay Gupta We consider the classes M fi and N fị of the analytic functions and two general integral operators. We prove some properties for these operators on these classes. Copyright 2008 Daniel Breaz. 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 U z C z 1 be the open unit disk and let A denote the class of the functions f z of the form f z z a2z2 a3z3 z U 1-1 which are analytic in the open disk U. Let M f be the subclass of A consisting of the functions f z which satisfy the inequality f zf r z i Re f z U f 1 I f z 1-2 and let N f be the subclass of A consisting of functions f z which satisfy the inequality f zf z i r 7Ta 1 f z U. I f z 1-3 These classes are studied by Uralegaddi et al- in 1 and Owa and Srivastava in 2 . Consider the integral operator Fn introduced by D- Breaz and N- Breaz in 3 having the form Fn z fz f r ỊỊÌVdt Fn z - 0 t t j M 1-4 where fi z A and ai 0 for all i 1 . n - 2 Journal of Inequalities and Applications Remark . This operator extends the integral operator of Alexander given by F z .Cơ 0 0 . Also we consider the next integral operator denoted by Fa1 .an that was introduced by Breaz et al. in 4 having the form fZ Fa1 a z f1 w a1 fn 0 andt 0 where fi z G A and ai 0 for all i G 1 . n . It is easy to see that these integral operators are analytic operators. 2. Main results Theorem . Let fi

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