Subordinations for domains bounded by conic sections

Kanas, Stanisława

Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 589-598 / Harvested from Project Euclid

Résumé

We establish some conditions under which the differential subordination of the type $p(z) + zp'(z)/p(z) \prec Q(z)$ yields $p \prec q$ in $\mathcal U$. Functions $Q$ and $q$ are chosen so that they map the unit disk onto domains enclosed by conic sections. Some applications of obtained results are given.

Publié le : 2008-05-15
Classification: univalent functions, uniformly convex functions, $k$-uniformly convex functions, $k$-starlike functions, differential subordination, 30C45

@article{1225893941,
     author = {Kanas, Stanis\l awa},
     title = {Subordinations for domains bounded by conic sections},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 589-598},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1225893941}
}

Kanas, Stanisława. Subordinations for domains bounded by conic sections. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  589-598. http://gdmltest.u-ga.fr/item/1225893941/