Properties of functions concerned with Caratheodory functions

• Autorzy: Mamoru Nunokawa , Emel Yavuz Duman , Shigeyoshi Owa
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Analytic; starlike; Caratheodory function.

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2013
• Tom: 67
• Numer: 2

Daty

wydano

2013

online

2015-07-15

Twórcy

autor

Mamoru Nunokawa

autor

Emel Yavuz Duman

autor

Shigeyoshi Owa

Bibliografia

• Caratheodory, C., Uber den Variabilitatsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64(1907), 95–115.
• Jack, I. S., Functions starlike and convex of order \(\alpha\), J. London Math. Soc. 3 (1971), 469–474.
• Miller, S. S., Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289–305.
• Nunokawa, M., On the Bazilevic analytic functions, Sci. Rep. Fac. Edu. Gunma Univ. 21 (1972), 9–13.
• Obradovic, M., Owa, S., A criterion for starlikeness, Math. Nachr. 140 (1989), 97–102.
• Umezawa, T., Analytic functions convex in one direction, J. Math. Soc. Japan 4 (1952), 194–202.

Identyfikatory

DOI

10.17951/a.2013.67.2.33-41