Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions , 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.
@article{bwmeta1.element.bwnjournal-article-apmv55z1p81bwm, author = {G. Dimkov and J. Stankiewicz and Z. Stankiewicz}, title = {On a class of starlike functions defined in a halfplane}, journal = {Annales Polonici Mathematici}, volume = {55}, year = {1991}, pages = {81-86}, zbl = {0769.30006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p81bwm} }
G. Dimkov; J. Stankiewicz; Z. Stankiewicz. On a class of starlike functions defined in a halfplane. Annales Polonici Mathematici, Tome 55 (1991) pp. 81-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p81bwm/
[000] [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). | Zbl 0199.40001
[001] [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).
[002] [3] J. Stankiewicz and Z. Stankiewicz, On the classes of functions regular in a halfplane I, Bull. Polish Acad. Sci. Math., to appear. | Zbl 0757.30016
[003] [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.