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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyperbolic convexity and the analytic fixed point function
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by Alexander Yu. Solynin PDF
Proc. Amer. Math. Soc. 135 (2007), 1181-1186 Request permission

Abstract:

We answer a question raised by D. Mejía and Ch. Pommerenke by showing that the analytic fixed point function is hyperbolically convex in the unit disc.
References
  • Barbara Brown Flinn, Hyperbolic convexity and level sets of analytic functions, Indiana Univ. Math. J. 32 (1983), no. 6, 831–841. MR 721566, DOI 10.1512/iumj.1983.32.32056
  • Seán Dineen, The Schwarz lemma, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Oxford Science Publications. MR 1033739
  • V. N. Dubinin, Symmetrization in the geometric theory of functions of a complex variable, Uspekhi Mat. Nauk 49 (1994), no. 1(295), 3–76 (Russian); English transl., Russian Math. Surveys 49 (1994), no. 1, 1–79. MR 1307130, DOI 10.1070/RM1994v049n01ABEH002002
  • Frederick P. Gardiner and Nikola Lakic, Quasiconformal Teichmüller theory, Mathematical Surveys and Monographs, vol. 76, American Mathematical Society, Providence, RI, 2000. MR 1730906, DOI 10.1090/surv/076
  • W. K. Hayman, Subharmonic functions. Vol. 2, London Mathematical Society Monographs, vol. 20, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1989. MR 1049148
  • Vilhelm Jørgensen, On an inequality for the hyperbolic measure and its applications in the theory of functions, Math. Scand. 4 (1956), 113–124. MR 84584, DOI 10.7146/math.scand.a-10460
  • Diego Mejía and Christian Pommerenke, The analytic fixed point function in the disk, Comput. Methods Funct. Theory 5 (2005), no. 2, 275–299. MR 2205415, DOI 10.1007/BF03321099
  • D. Mejía, Ch. Pommerenke, The analytic point function II. Preprint.
  • A. Yu. Solynin, Continuous symmetrization of sets, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 185 (1990), no. Anal. Teor. Chisel i Teor. Funktsiĭ. 10, 125–139, 186 (Russian); English transl., J. Soviet Math. 59 (1992), no. 6, 1214–1221. MR 1097593, DOI 10.1007/BF01374083
  • A. Yu. Solynin, Polarization and functional inequalities, Algebra i Analiz 8 (1996), no. 6, 148–185 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 8 (1997), no. 6, 1015–1038. MR 1458141
  • A. Yu. Solynin and M. Vuorinen, Estimates for the hyperbolic metric of the punctured plane and applications, Israel J. Math. 124 (2001), 29–60. MR 1856503, DOI 10.1007/BF02772606
  • René P. Sperb, Maximum principles and their applications, Mathematics in Science and Engineering, vol. 157, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 615561
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Additional Information
  • Alexander Yu. Solynin
  • Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
  • MR Author ID: 206458
  • Email: alex.solynin@ttu.edu
  • Received by editor(s): November 17, 2005
  • Published electronically: October 18, 2006
  • Additional Notes: This research was supported in part by NSF grant DMS-0412908
  • Communicated by: Juha M. Heinonen
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 1181-1186
  • MSC (2000): Primary 30C55, 30F45
  • DOI: https://doi.org/10.1090/S0002-9939-06-08661-8
  • MathSciNet review: 2262924