On a class of starlike functions defined in a halfplane

G. Dimkov; J. Stankiewicz; Z. Stankiewicz

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 81-86
  • ISSN: 0066-2216

Abstract

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Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions l i m D ∋ z → ∞ ( f ( z ) - z ) = a , a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.

How to cite

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G. Dimkov, J. Stankiewicz, and Z. Stankiewicz. "On a class of starlike functions defined in a halfplane." Annales Polonici Mathematici 55.1 (1991): 81-86. <http://eudml.org/doc/262406>.

@article{G1991,
abstract = {Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions $lim_\{D ∋ z → ∞\}(f(z) - z) = a$, a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.},
author = {G. Dimkov, J. Stankiewicz, Z. Stankiewicz},
journal = {Annales Polonici Mathematici},
keywords = {starlike functions},
language = {eng},
number = {1},
pages = {81-86},
title = {On a class of starlike functions defined in a halfplane},
url = {http://eudml.org/doc/262406},
volume = {55},
year = {1991},
}

TY - JOUR
AU - G. Dimkov
AU - J. Stankiewicz
AU - Z. Stankiewicz
TI - On a class of starlike functions defined in a halfplane
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 81
EP - 86
AB - Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions $lim_{D ∋ z → ∞}(f(z) - z) = a$, a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.
LA - eng
KW - starlike functions
UR - http://eudml.org/doc/262406
ER -

References

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  1. [1] I. A. Aleksandrov and V. V. Sobolev, Extremal problems for some classes of univalent functions in the halfplane, Ukrain. Mat. Zh. 22 (3) (1970), 291-307 (in Russian). Zbl0199.40001
  2. [2] V. G. Moskvin, T. N. Selakhova and V. V. Sobolev, Extremal properties of some classes of conformal self-mappings of the halfplane with fixed coefficients, Sibirsk. Mat. Zh. 21 (2) (1980), 139-154 (in Russian). 
  3. [3] J. Stankiewicz and Z. Stankiewicz, On the classes of functions regular in a halfplane I, Bull. Polish Acad. Sci. Math., to appear. Zbl0757.30016
  4. [4] J. Stankiewicz and Z. Stankiewicz, On the classes of functions regular in a halfplane II, Folia Sci. Univ. Techn. Resoviensis Mat. Fiz. 60 (9) (1989), 111-123. 

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