Properties of functions concerned with Caratheodory functions

Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa


Let \(\mathcal{P}_n\) denote the class of analytic functions \(p(z)\) of the form \(p(z)=1+c_nz^n+c_{n+1}z^{n+1}+\dots\) in the open unit disc \(\mathbb{U}\). Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for \(p(z)\) concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.


Analytic; starlike; Caratheodory function.

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Data publikacji: 2015-07-15 00:00:00
Data złożenia artykułu: 2016-01-12 09:25:02


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