Properties of functions concerned with Caratheodory functions

Mamoru Nunokawa; Emel Yavuz Duman; Shigeyoshi Owa

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2013)

  • Volume: 67, Issue: 2
  • ISSN: 0365-1029

Abstract

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Let 𝒫 n denote the class of analytic functions p ( z ) of the form p ( z ) = 1 + c n z n + c n + 1 z 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.

How to cite

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Mamoru Nunokawa, Emel Yavuz Duman, and Shigeyoshi Owa. "Properties of functions concerned with Caratheodory functions." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 67.2 (2013): null. <http://eudml.org/doc/289787>.

@article{MamoruNunokawa2013,
abstract = {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.},
author = {Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Analytic; starlike; Caratheodory function.},
language = {eng},
number = {2},
pages = {null},
title = {Properties of functions concerned with Caratheodory functions},
url = {http://eudml.org/doc/289787},
volume = {67},
year = {2013},
}

TY - JOUR
AU - Mamoru Nunokawa
AU - Emel Yavuz Duman
AU - Shigeyoshi Owa
TI - Properties of functions concerned with Caratheodory functions
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2013
VL - 67
IS - 2
SP - null
AB - 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.
LA - eng
KW - Analytic; starlike; Caratheodory function.
UR - http://eudml.org/doc/289787
ER -

References

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  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 α , 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. 

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