subordination result
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2015 ◽  
Vol 220 ◽  
pp. 45-66 ◽  
Author(s):  
Masaki Izumi ◽  
Yoshimichi Ueda

AbstractThe present notes provide a proof of i* (ℂP + ℂ(I - P); ℂQ + ℂ(I - Q)) = – χorb(P,Q) for any pair of projections P,Q with τ(P) = τ(Q) = 1/2. The proof includes new extra observations, such as a subordination result in terms of Loewner equations. A study of the general case is also given.


2015 ◽  
Vol 220 ◽  
pp. 45-66
Author(s):  
Masaki Izumi ◽  
Yoshimichi Ueda

AbstractThe present notes provide a proof ofi* (ℂP + ℂ(I - P); ℂQ + ℂ(I - Q))= – χorb(P,Q) foranypair of projectionsP,Qwithτ(P) = τ(Q) = 1/2. The proof includes new extra observations, such as a subordination result in terms of Loewner equations. A study of the general case is also given.


Author(s):  
E. A. Oyekan ◽  
T. O. Opoola

AbstractIn this paper we discuss some subordination results for a subclass of functions analytic in the unit disk U


2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Saibah Siregar ◽  
Maslina Darus

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.


Author(s):  
A. A. Attiya ◽  
Nak Eun Cho ◽  
M. A. Kutbi

The purpose of the present paper is to derive a subordination result for functions in the class of normalized analytic functions in the open unit disk . A number of interesting applications of the subordination result are also considered.


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