# Certain partial differential subordinations on some Reinhardt domains in ${\u2102}^{n}$

Annales Polonici Mathematici (1997)

- Volume: 65, Issue: 2, page 179-191
- ISSN: 0066-2216

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topGabriela Kohr, and Mirela Kohr. "Certain partial differential subordinations on some Reinhardt domains in $ℂ^n$." Annales Polonici Mathematici 65.2 (1997): 179-191. <http://eudml.org/doc/269941>.

@article{GabrielaKohr1997,

abstract = {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 $B_\{2p\}$ with p ≥ 1.},

author = {Gabriela Kohr, Mirela Kohr},

journal = {Annales Polonici Mathematici},

keywords = {subordination; biholomorphic mapping; Reinhardt domain; holomorphic mappings; Reinhardt domains},

language = {eng},

number = {2},

pages = {179-191},

title = {Certain partial differential subordinations on some Reinhardt domains in $ℂ^n$},

url = {http://eudml.org/doc/269941},

volume = {65},

year = {1997},

}

TY - JOUR

AU - Gabriela Kohr

AU - Mirela Kohr

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

JO - Annales Polonici Mathematici

PY - 1997

VL - 65

IS - 2

SP - 179

EP - 191

AB - 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 $B_{2p}$ with p ≥ 1.

LA - eng

KW - subordination; biholomorphic mapping; Reinhardt domain; holomorphic mappings; Reinhardt domains

UR - http://eudml.org/doc/269941

ER -

## References

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- [KO3] G. Kohr and P. Liczberski, General partial differential subordinations for holomorphic mappings in ${\u2102}^{n}$, Math. Nachr., to appear. Zbl1011.32011
- [KO4] G. Kohr and C. Pintea, An extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined on some domains in ${\u2102}^{n}$, to appear. Zbl0881.32012
- [L] P. Liczberski, Jack’s Lemma for holomorphic mappings in ${\u2102}^{n}$, Ann. Univ. Mariae Curie-Skłodowska Sect. A 40 (1986), 131-140.
- [MM1] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289-305. Zbl0367.34005
- [MM2] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations 67 (1987), 199-211. Zbl0633.34005
- [S1] T. J. Suffridge, The principle of subordination applied to functions of several variables, Pacific J. Math. 33 (1970), 241-248. Zbl0196.09601
- [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.

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