On the univalent, bounded, non-vanishing and symmetric functions in the unit disk
J. Śladkowska
Annales Polonici Mathematici, Tome 63 (1996), p. 291-299 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:269965 
@article{bwmeta1.element.bwnjournal-article-apmv64z3p291bwm,
     author = {J. \'Sladkowska},
     title = {On the univalent, bounded, non-vanishing and symmetric functions in the unit disk},
     journal = {Annales Polonici Mathematici},
     volume = {63},
     year = {1996},
     pages = {291-299},
     zbl = {0860.30021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p291bwm}
}

J. Śladkowska. On the univalent, bounded, non-vanishing and symmetric functions in the unit disk. Annales Polonici Mathematici, Tome 63 (1996) pp. 291-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p291bwm/

[000] [1] G. M. Goluzin, Geometric Theory of a Complex Variable, Transl. Math. Monographs 26, Amer. Math. Soc., Providence, R.I., 1969. | Zbl 0183.07502

[001] [2] J. A. Hummel and B. Pinchuk, Variations for bounded nonvanishing univalent functions, J. Anal. Math. 44 (1984-85), 183-199.

[002] [3] J. A. Hummel and M. M. Schiffer, Variational methods for Bieberbach-Eilenberg functions and for pairs, Ann. Acad. Sci. Fenn. Ser. AI Math. 3 (1977), 3-42. | Zbl 0379.30011

[003] [4] C. Pommerenke, Univalent Functions, Göttingen, 1975.

[004] [5] D. V. Prokhorov and J. Szynal, Coefficient estimates for bounded nonvanishing functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 223-230. | Zbl 0469.30016

[005] [6] J. Śladkowska, Sur une famille des fonctions univalentes et bornées, Demonstratio Math. 22 (1989), 973-982. | Zbl 0712.30020

[006] [7] J. Śladkowska, Sur la famille des fonctions univalentes, bornées et symétriques qui n'atteignent pas une valeur fixée, Ann. Polon. Math. 52 (1990), 147-160. | Zbl 0718.30014

[007] [8] J. Śladkowska, A variational method for univalent nonvanishing functions in the unit disk, Folia Sci. Univ. Tech. Resov. 129, Math. 16 (1994), 63-77. | Zbl 0863.30031