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

Abstract

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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.

How to cite

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Mamoru 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

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  1. [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. [2] Jack, I. S., Functions starlike and convex of order α, J. London Math. Soc. 3 (1971), 469-474.[Crossref] Zbl0224.30026
  3. [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. [4] Nunokawa, M., On the Bazilević analytic functions, Sci. Rep. Fac. Edu. Gunma Univ. 21 (1972), 9-13. 
  5. [5] Obradović, M., Owa, S., A criterion for starlikeness, Math. Nachr. 140 (1989), 97-102.[Crossref] Zbl0676.30009
  6. [6] Umezawa, T., Analytic functions convex in one direction, J. Math. Soc. Japan 4 (1952), 194-202. Zbl0047.31801

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