# On the coefficient bodies of meromorphic univalent functions omitting a disc

Annales Polonici Mathematici (2000)

- Volume: 75, Issue: 1, page 47-58
- ISSN: 0066-2216

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topTammi, Olli. "On the coefficient bodies of meromorphic univalent functions omitting a disc." Annales Polonici Mathematici 75.1 (2000): 47-58. <http://eudml.org/doc/208383>.

@article{Tammi2000,

abstract = {Let S(b) be the class of bounded normalized univalent functions and Σ(b) the class of normalized univalent meromorphic functions omitting a disc with radius b. The close connection between these classes allows shifting the coefficient body information from the former to the latter. The first non-trivial body can be determined in Σ(b) as well as the next one in the real subclass $Σ_\{R\}(b)$.},

author = {Tammi, Olli},

journal = {Annales Polonici Mathematici},

keywords = {coefficient bodies; univalent functions},

language = {eng},

number = {1},

pages = {47-58},

title = {On the coefficient bodies of meromorphic univalent functions omitting a disc},

url = {http://eudml.org/doc/208383},

volume = {75},

year = {2000},

}

TY - JOUR

AU - Tammi, Olli

TI - On the coefficient bodies of meromorphic univalent functions omitting a disc

JO - Annales Polonici Mathematici

PY - 2000

VL - 75

IS - 1

SP - 47

EP - 58

AB - Let S(b) be the class of bounded normalized univalent functions and Σ(b) the class of normalized univalent meromorphic functions omitting a disc with radius b. The close connection between these classes allows shifting the coefficient body information from the former to the latter. The first non-trivial body can be determined in Σ(b) as well as the next one in the real subclass $Σ_{R}(b)$.

LA - eng

KW - coefficient bodies; univalent functions

UR - http://eudml.org/doc/208383

ER -

## References

top- [1] Charzyński, Z.: and Janowski, W.:, Domaine de variation des coefficients ${A}_{2}$ et ${A}_{3}$ des functions univalentes et bornées, Bull. Soc. Sci. Lettres Łódź 10 (1959), no. 5. Zbl0227.30016
- [2] Jokinen, O.: and Tammi, O.:, On determining the points of the second coefficient body $({a}_{4},{a}_{3},{a}_{2})$ for bounded real univalent functions, Kodai Math. J. 17 (1994), 82-100. Zbl0805.30013
- [3] Kortram, R.: and Tammi, O.:, On the first coefficient regions of bounded univalent functions, Ann. Acad. Sci. Fenn. Ser. A I 592 (1974). Zbl0305.30019
- [4] Netanyahu, E.:, Extremal problems for schlicht functions in the exterior of the unit circle, Canad. J. Math. 17 (1965), 335-341. Zbl0148.30804
- [5] Schaeffer, A. C. : and Spencer, D. C.:, Coefficient Regions for Schlicht Functions, Amer. Math. Soc. Colloq. Publ. 35, 1950.
- [6] Siejka, H.:, On meromorphic univalent functions omitting a disc, Israel J. Math. 54 (1986), 291-299. Zbl0608.30020
- [7] Śladkowska, J.:, Estimations of the second coefficient of a univalent, bounded, symmetric and non-vanishing function by means of Loewner's parametric method, Ann. Polon. Math. 68 (1998), 119-123. Zbl0905.30012
- [8] Tammi, O.:, Extremum Problems for Bounded Univalent Functions, Lecture Notes in Math. 646, Springer, Berlin, 1978. Zbl0375.30006
- [9] Tammi, O.: Extremum Problems for Bounded Univalent Functions II, Lecture Notes in Math. 913, Springer, Berlin, 1982. Zbl0481.30020
- [10] Tammi, O.: On the first coefficient bodies of bounded real non-vanishing univalent functions, Ann. Univ. Mariae Curie-Skłodowska 52 (1998), 177-190. Zbl1009.30012

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