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1996-1997 | 65 | 2 | 179-191
Tytuł artykułu

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

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Abstrakty
EN
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.
Twórcy
  • Faculty of Mathematics, Babeş-Bolyai University,1 M. Kogălniceanu Str., 3400 Cluj-Napoca, Romania
autor
  • Faculty of Mathematics, Babeş-Bolyai University,1 M. Kogălniceanu Str., 3400 Cluj-Napoca, Romania
Bibliografia
  • [C] B. Chabat, Introduction à l'analyse complexe, tome II, Mir, Moscou, 1990.
  • [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.
  • [GWQ] S. Gong, S. K. Wang and Q. Yu, Biholomorphic convex mappings of ball in $ℂ^n$, Pacific J. Math. 161 (1993), 287-306.
  • [K] K. Kikuchi, Starlike and convex mappings in several complex variables, Pacific J. Math. 44 (1973), 569-580.
  • [KO1] G. Kohr, On some partial differential subordinations for holomorphic mappings in $ℂ^n$, Libertas Math. 115 (1996), 129-142.
  • [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.
  • [KO3] G. Kohr and P. Liczberski, General partial differential subordinations for holomorphic mappings in $ℂ^n$, Math. Nachr., to appear.
  • [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.
  • [L] P. Liczberski, Jack's Lemma for holomorphic mappings in $ℂ^n$, 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.
  • [MM2] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations 67 (1987), 199-211.
  • [S1] T. J. Suffridge, The principle of subordination applied to functions of several variables, Pacific J. Math. 33 (1970), 241-248.
  • [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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bwmeta1.element.bwnjournal-article-apmv65z2p179bwm
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