Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 939-948

JULIA'S LEMMA ON THE HYPERBOLIC DISK

Árpád Baricz, Saminathan Ponnusamy and Csaba Varga

Babes-Bolyai University, Department of Economics, Cluj-Napoca 400591, Romania
and Óbuda University, Institute of Applied Mathematics
1034 Budapest, Hungary; bariczocsi 'at' yahoo.com

Indian Statistical Institute (ISI), Chennai Centre, SETS, MGR Knowledge City
CIT Campus, Taramani, Chennai 600 113, India; samy 'at' isichennai.res.in, samy 'at' iitm.ac.in

Babes-Bolyai University, Faculty of Mathematics and Computer Science
400084 Cluj-Napoca, Romania; csvarga 'at' cs.ubbcluj.ro

Abstract. This paper contains an extension of the Julia-Miller-Mocanu lemma for holomorphic functions defined on the unit disk D endowed by the hyperbolic metric on D. The extension is made by following on the one hand the way of the differential subordinations theory and on the other hand the method of Lagrange multipliers, like in an extension of the Julia-Miller-Mocanu lemma for holomorphic mappings in Cⁿ.

2010 Mathematics Subject Classification: Primary 32H02, 30F45, 42B15.

Key words: Holomorphic functions, hyperbolic metric, Lagrange multipliers.

Reference to this article: Á. Baricz, S. Ponnusamy and C. Varga: Julia's lemma on the hyperbolic disk. Ann. Acad. Sci. Fenn. Math. 40 (2015), 939-948.

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doi:10.5186/aasfm.2015.4054