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 .
@article{bwmeta1.element.bwnjournal-article-apmv75z1p47bwm, author = {Tammi, Olli}, title = {On the coefficient bodies of meromorphic univalent functions omitting a disc}, journal = {Annales Polonici Mathematici}, volume = {75}, year = {2000}, pages = {47-58}, zbl = {0967.30006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv75z1p47bwm} }
Tammi, Olli. On the coefficient bodies of meromorphic univalent functions omitting a disc. Annales Polonici Mathematici, Tome 75 (2000) pp. 47-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv75z1p47bwm/
[000] [1] Charzyński, Z.: and Janowski, W.:, Domaine de variation des coefficients et des functions univalentes et bornées, Bull. Soc. Sci. Lettres Łódź 10 (1959), no. 5. | Zbl 0227.30016
[001] [2] Jokinen, O.: and Tammi, O.:, On determining the points of the second coefficient body for bounded real univalent functions, Kodai Math. J. 17 (1994), 82-100. | Zbl 0805.30013
[002] [3] Kortram, R.: and Tammi, O.:, On the first coefficient regions of bounded univalent functions, Ann. Acad. Sci. Fenn. Ser. A I 592 (1974). | Zbl 0305.30019
[003] [4] Netanyahu, E.:, Extremal problems for schlicht functions in the exterior of the unit circle, Canad. J. Math. 17 (1965), 335-341. | Zbl 0148.30804
[004] [5] Schaeffer, A. C. : and Spencer, D. C.:, Coefficient Regions for Schlicht Functions, Amer. Math. Soc. Colloq. Publ. 35, 1950.
[005] [6] Siejka, H.:, On meromorphic univalent functions omitting a disc, Israel J. Math. 54 (1986), 291-299. | Zbl 0608.30020
[006] [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. | Zbl 0905.30012
[007] [8] Tammi, O.:, Extremum Problems for Bounded Univalent Functions, Lecture Notes in Math. 646, Springer, Berlin, 1978. | Zbl 0375.30006
[008] [9] Tammi, O.: Extremum Problems for Bounded Univalent Functions II, Lecture Notes in Math. 913, Springer, Berlin, 1982. | Zbl 0481.30020
[009] [10] Tammi, O.: On the first coefficient bodies of bounded real non-vanishing univalent functions, Ann. Univ. Mariae Curie-Skłodowska 52 (1998), 177-190. | Zbl 1009.30012