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Schwarz-Pick-type estimates for the hyperbolic derivative
Journal of Inequalities and Applications volume 2006, Article number: 96368 (2006)
Abstract
We obtain Schwarz-Pick-type estimates for the hyperbolic derivative of an analytic self-map of the unit disk in.
References
Beardon AF: The Schwarz-Pick lemma for derivatives. Proceedings of the American Mathematical Society 1997,125(11):3255–3256. 10.1090/S0002-9939-97-03906-3
Duren PL: Univalent Functions, Fundamental Principles of Mathematical Sciences. Volume 259. Springer, New York; 1983:xiv+382.
Kaptanoğlu HT: Some refined Schwarz-Pick lemmas. The Michigan Mathematical Journal 2002,50(3):649–664.
Mercer PR: Sharpened versions of the Schwarz lemma. Journal of Mathematical Analysis and Applications 1997,205(2):508–511. 10.1006/jmaa.1997.5217
Mercer PR: Another look at Julia's lemma. Complex Variables 2000,43(2):129–138.
Yamashita S: The Pick version of the Schwarz lemma and comparison of the Poincaré densities. Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1994,19(2):291–322.
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Mercer, P.R. Schwarz-Pick-type estimates for the hyperbolic derivative. J Inequal Appl 2006, 96368 (2006). https://doi.org/10.1155/JIA/2006/96368
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DOI: https://doi.org/10.1155/JIA/2006/96368