# Properties of functions concerned with Carathéodory functions

Mamoru Nunokawa; Emel Yavuz; Shigeyoshi Owa

Annales UMCS, Mathematica (2013)

- Volume: 67, Issue: 2, page 33-41
- ISSN: 2083-7402

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topMamoru Nunokawa, Emel Yavuz, and Shigeyoshi Owa. "Properties of functions concerned with Carathéodory functions." Annales UMCS, Mathematica 67.2 (2013): 33-41. <http://eudml.org/doc/268151>.

@article{MamoruNunokawa2013,

abstract = {Let Pn denote the class of analytic functions p(z) of the form p(z) = 1+cnzn + cn+1zn+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 Carath´eodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradović and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.},

author = {Mamoru Nunokawa, Emel Yavuz, Shigeyoshi Owa},

journal = {Annales UMCS, Mathematica},

keywords = {Analytic; starlike; Carathéodory function; starlike function},

language = {eng},

number = {2},

pages = {33-41},

title = {Properties of functions concerned with Carathéodory functions},

url = {http://eudml.org/doc/268151},

volume = {67},

year = {2013},

}

TY - JOUR

AU - Mamoru Nunokawa

AU - Emel Yavuz

AU - Shigeyoshi Owa

TI - Properties of functions concerned with Carathéodory functions

JO - Annales UMCS, Mathematica

PY - 2013

VL - 67

IS - 2

SP - 33

EP - 41

AB - Let Pn denote the class of analytic functions p(z) of the form p(z) = 1+cnzn + cn+1zn+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 Carath´eodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradović and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

LA - eng

KW - Analytic; starlike; Carathéodory function; starlike function

UR - http://eudml.org/doc/268151

ER -

## References

top- [1] Carathéodory, C., Uber den Variabilitatsbereich der Koeffizienten von Potenzreihen,die gegebene Werte nicht annehmen, Math. Ann. 64(1907), 95-115.[Crossref] Zbl38.0448.01
- [2] Jack, I. S., Functions starlike and convex of order α, J. London Math. Soc. 3 (1971), 469-474.[Crossref] Zbl0224.30026
- [3] Miller, S. S., Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289-305.[Crossref] Zbl0367.34005
- [4] Nunokawa, M., On the Bazilević analytic functions, Sci. Rep. Fac. Edu. Gunma Univ. 21 (1972), 9-13.
- [5] Obradović, M., Owa, S., A criterion for starlikeness, Math. Nachr. 140 (1989), 97-102.[Crossref] Zbl0676.30009
- [6] Umezawa, T., Analytic functions convex in one direction, J. Math. Soc. Japan 4 (1952), 194-202. Zbl0047.31801

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