Certain partial differential subordinations on some Reinhardt domains in $ℂ^n$

Gabriela Kohr; Mirela Kohr

Certain partial differential subordinations on some Reinhardt domains in

ℂ^{n}

Gabriela Kohr ; Mirela Kohr

Annales Polonici Mathematici, Tome 66 (1997), p. 179-191 / Harvested from The Polish Digital Mathematics Library

Access to full text
Full (PDF)

Résumé

We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in $ℂ^{n}$ . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain $B_{2 p}$ with p ≥ 1.

Publié le : 1997-01-01

Zbl 0872.32003

EUDML-ID : urn:eudml:doc:269941

@article{bwmeta1.element.bwnjournal-article-apmv65z2p179bwm,
     author = {Gabriela Kohr and Mirela Kohr},
     title = {Certain partial differential subordinations on some Reinhardt domains in $$\mathbb{C}$^n$
            },
     journal = {Annales Polonici Mathematici},
     volume = {66},
     year = {1997},
     pages = {179-191},
     zbl = {0872.32003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv65z2p179bwm}
}

Gabriela Kohr; Mirela Kohr. Certain partial differential subordinations on some Reinhardt domains in $ℂ^n$
            . Annales Polonici Mathematici, Tome 66 (1997) pp. 179-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv65z2p179bwm/

Bibliographie

[000] [C] B. Chabat, Introduction à l'analyse complexe, tome II, Mir, Moscou, 1990.

[001] [GW] S. Gong and S. K. Wang, A necessary and sufficient condition that biholomorphic mappings are starlike on a class of Reinhardt domains, Chinese Ann. Math. Ser. B 13 (1) (1992), 95-104. | Zbl 0793.32001

[002] [GWQ] S. Gong, S. K. Wang and Q. Yu, Biholomorphic convex mappings of ball in $ℂ^{n}$ , Pacific J. Math. 161 (1993), 287-306. | Zbl 0788.32017

[003] [K] K. Kikuchi, Starlike and convex mappings in several complex variables, Pacific J. Math. 44 (1973), 569-580. | Zbl 0262.32009

[004] [KO1] G. Kohr, On some partial differential subordinations for holomorphic mappings in $ℂ^{n}$ , Libertas Math. 115 (1996), 129-142.

[005] [KO2] G. Kohr and M. Kohr-Ile, Partial differential subordinations for holomorphic mappings of several complex variables, Studia Univ. Babeş-Bolyai Math. 60 (4) (1995), 46-62. | Zbl 0862.32017

[006] [KO3] G. Kohr and P. Liczberski, General partial differential subordinations for holomorphic mappings in $ℂ^{n}$ , Math. Nachr., to appear. | Zbl 1011.32011

[007] [KO4] G. Kohr and C. Pintea, An extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined on some domains in $ℂ^{n}$ , to appear. | Zbl 0881.32012

[008] [L] P. Liczberski, Jack’s Lemma for holomorphic mappings in $ℂ^{n}$ , Ann. Univ. Mariae Curie-Skłodowska Sect. A 40 (1986), 131-140.

[009] [MM1] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289-305. | Zbl 0367.34005

[010] [MM2] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations 67 (1987), 199-211. | Zbl 0633.34005

[011] [S1] T. J. Suffridge, The principle of subordination applied to functions of several variables, Pacific J. Math. 33 (1970), 241-248. | Zbl 0196.09601

[012] [S2] T. J. Suffridge, Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions, in: Lecture Notes in Math. 599, Springer, 1976, 146-159.