Geodesic
Properties of functions concerned with Caratheodory functions
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 67 (2013) no. 2 Cet article a éte moissonné depuis la source Library of Science

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Let 𝒫_n denote the class of analytic functions p(z) of the form p(z)=1+c_nz^n+c_n+1z^n+1+… in the open unit disc 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.
Keywords: Analytic, starlike, Caratheodory function. 
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Nunokawa, Mamoru; Duman, Emel Yavuz; Owa, Shigeyoshi. Properties of functions concerned with Caratheodory functions. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 67 (2013) no. 2. http://geodesic.mathdoc.fr/item/AUM_2013_67_2_a4/

[1] Caratheodory, C., Uber den Variabilitatsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64(1907), 95–115.

[2] Jack, I. S., Functions starlike and convex of order \(\alpha\), J. London Math. Soc. 3 (1971), 469–474.

[3] Miller, S. S., Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289–305.

[4] Nunokawa, M., On the Bazilevic analytic functions, Sci. Rep. Fac. Edu. Gunma Univ. 21 (1972), 9–13.

[5] Obradovic, M., Owa, S., A criterion for starlikeness, Math. Nachr. 140 (1989), 97–102.

[6] Umezawa, T., Analytic functions convex in one direction, J. Math. Soc. Japan 4 (1952), 194–202.