한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제27권4호
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  • Pages.157-169
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  • 2020
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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APPLICATIONS OF SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA

  • 투고 : 2019.03.12
  • 심사 : 2020.11.06
  • 발행 : 2020.11.30
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초록

In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

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참고문헌

  1. T. Akyel & B.N. Ornek: A Sharp Schwarz lemma at the boundary. J. Korean Soc. Math. Ser. B: Pure Appl. Math. 22 (2015), no. 3, 263-273.
  2. T.A. Azero glu & B.N. Ornek: A refined Schwarz inequality on the boundary. Complex Variables and Elliptic Equations 58 (2013), 571-577. https://doi.org/10.1080/17476933.2012.718338
  3. H.P. Boas: Julius and Julia: Mastering the Art of the Schwarz lemma. Amer. Math. Monthly 117 (2010), 770-785. https://doi.org/10.4169/000298910x521643
  4. V.N. Dubinin: The Schwarz inequality on the boundary for functions regular in the disc. J. Math. Sci. 122 (2004), 3623-3629. https://doi.org/10.1023/B:JOTH.0000035237.43977.39
  5. G.M. Golusin: Geometric Theory of Functions of Complex Variable [in Russian]. 2nd edn., Moscow 1966.
  6. I.S. Jack: Functions starlike and convex of order α. J. London Math. Soc. 3 (1971), 469-474. https://doi.org/10.1112/jlms/s2-3.3.469
  7. M. Jeong: The Schwarz lemma and its applications at a boundary point. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 21 (2014), 275-284.
  8. M. Jeong: The Schwarz lemma and boundary fixed points. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 18 (2011), 219-227.
  9. M. Mateljevic: Rigidity of holomorphic mappings & Schwarz and Jack lemma. DOI:10.13140/RG.2.2.34140.90249, In press.
  10. P.R. Mercer: Sharpened Versions of the Schwarz Lemma. J. Math. Anal. Appl. 205 (1997), 508-511. https://doi.org/10.1006/jmaa.1997.5217
  11. P.R. Mercer: Boundary Schwarz inequalities arising from Rogosinski's lemma. Journal of Classical Analysis 12 (2018), 93-97. https://doi.org/10.7153/jca-2018-12-08
  12. P.R. Mercer: An improved Schwarz Lemma at the boundary. Open Mathematics 16 (2018), 1140-1144. https://doi.org/10.1515/math-2018-0096
  13. R. Osserman: A sharp Schwarz inequality on the boundary. Proc. Amer. Math. Soc. 128 (2000) 3513-3517. https://doi.org/10.1090/S0002-9939-00-05463-0
  14. B.N. Ornek & T. Duzenli: Bound Estimates for the Derivative of Driving Point Impedance Functions. Filomat 32 (2018), no. 18, 6211-6218.. https://doi.org/10.2298/FIL1818211O
  15. B.N. Ornek & T. Dzenli: Boundary Analysis for the Derivative of Driving Point Impedance Functions. IEEE Transactions on Circuits and Systems II: Express Briefs 65 (2018), no. 9, 1149-1153. https://doi.org/10.1109/TCSII.2018.2809539
  16. B.N. Ornek: Sharpened forms of the Schwarz lemma on the boundary. Bull. Korean Math. Soc. 50 (2013), no. 6, 2053-2059. https://doi.org/10.4134/BKMS.2013.50.6.2053
  17. Ch. Pommerenke: Boundary Behaviour of Conformal Maps. Springer-Verlag, Berlin. 1992.