# On semi-typically real functions

Leopold Koczan; Katarzyna Trąbka-Więcław

Annales UMCS, Mathematica (2009)

- Volume: 63, Issue: 1, page 139-148
- ISSN: 2083-7402

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topLeopold Koczan, and Katarzyna Trąbka-Więcław. "On semi-typically real functions." Annales UMCS, Mathematica 63.1 (2009): 139-148. <http://eudml.org/doc/267841>.

@article{LeopoldKoczan2009,

abstract = {Suppose that A is the family of all functions that are analytic in the unit disk Δ and normalized by the condition [...] For a given A ⊂ A let us consider the following classes (subclasses of A): [...] and [...] where [...] and S consists of all univalent members of A.In this paper we investigate the case A = τ, where τ denotes the class of all semi-typically real functions, i.e. [...] We study relations between these classes. Furthermore, we find for them sets of variability of initial coeffcients, the sets of local univalence and the sets of typical reality.},

author = {Leopold Koczan, Katarzyna Trąbka-Więcław},

journal = {Annales UMCS, Mathematica},

keywords = {Typically real functions; sets of variability of coeffcients; typically real functions},

language = {eng},

number = {1},

pages = {139-148},

title = {On semi-typically real functions},

url = {http://eudml.org/doc/267841},

volume = {63},

year = {2009},

}

TY - JOUR

AU - Leopold Koczan

AU - Katarzyna Trąbka-Więcław

TI - On semi-typically real functions

JO - Annales UMCS, Mathematica

PY - 2009

VL - 63

IS - 1

SP - 139

EP - 148

AB - Suppose that A is the family of all functions that are analytic in the unit disk Δ and normalized by the condition [...] For a given A ⊂ A let us consider the following classes (subclasses of A): [...] and [...] where [...] and S consists of all univalent members of A.In this paper we investigate the case A = τ, where τ denotes the class of all semi-typically real functions, i.e. [...] We study relations between these classes. Furthermore, we find for them sets of variability of initial coeffcients, the sets of local univalence and the sets of typical reality.

LA - eng

KW - Typically real functions; sets of variability of coeffcients; typically real functions

UR - http://eudml.org/doc/267841

ER -

## References

top- Duren, P. L., Univalent Functions, Springer-Verlag, New York, 1983.
- Goluzin, G. M., On typically real functions, Mat. Sb. 27(69) (1950), 201-218 (Russian).
- Goodman, A. W., Univalent Functions, Mariner Publ. Co., Tampa, 1983.
- Koczan, L., On classes generated by bounded functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 52, no. 2 (1998), 95-101.
- Koczan, L., Szapiel, W., Extremal problems in some classes of measures. IV. Typically real functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 43 (1989), 55-68 (1991). Zbl0743.30023
- Koczan, L., Zaprawa, P., Koebe domains for the classes of functions with ranges included in given sets, J. Appl. Anal. 14, no. 1 (2008), 43-52. Zbl1153.30012
- Koczan, L., Zaprawa, P., On typically real functions with n-fold symmetry, Ann. Univ. Mariae Curie-Skłodowska Sect. A 52, no. 2 (1998), 103-112. Zbl1010.30019
- Zaprawa, P., On typically real bounded functions with n-fold symmetry, Folia Scientiarum Universitatis Technicae Resoviensis, Mathematics 21, no. 162 (1997), 151-160. Zbl0888.30014

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