Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SHARPENED FORMS OF THE SCHWARZ LEMMA ON THE BOUNDARY

  • Received : 2013.01.02
  • Published : 2013.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a boundary version of the Schwarz lemma is investigated. We obtain more general results at the boundary. Also, new inequalities of the Schwarz lemma at boundary is obtained and the sharpness of these inequalities is proved.

Keywords

References

  1. V. N. Dubinin, On the Schwarz inequality on the boundary for functions regular in the disk, J. Math. Sci. (N. Y.) 122 (2004), no. 6, 3623-3629. https://doi.org/10.1023/B:JOTH.0000035237.43977.39
  2. G. M. Golusin, Geometric Theory of Functions of Complex Variable, 2nd edn., Moscow 1966.
  3. A. I. Markushevich, Theory of Functions of a Complex Variable. Volume I, 1965.
  4. R. Osserman, A sharp Schwarz inequality on the boundary, Proc. Math. Soc. 128 (2000), no. 12, 3513-3517. https://doi.org/10.1090/S0002-9939-00-05463-0
  5. Ch. Pommerenke, Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.

Cited by

  1. Bounded Holomorphic Functions Covering No Concentric Circles vol.207, pp.6, 2015, https://doi.org/10.1007/s10958-015-2406-5
  2. Schwarz lemma at the boundary of the unit polydisk in ℂ n vol.58, pp.8, 2015, https://doi.org/10.1007/s11425-015-4975-7
  3. A SHARP SCHWARZ LEMMA AT THE BOUNDARY vol.22, pp.3, 2015, https://doi.org/10.7468/jksmeb.2015.22.3.263
  4. Sharpened forms of the generalized Schwarz inequality on the boundary vol.126, pp.1, 2016, https://doi.org/10.1007/s12044-015-0255-2
  5. THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT vol.21, pp.3, 2014, https://doi.org/10.7468/jksmeb.2014.21.3.219
  6. INEQUALITIES FOR THE NON-TANGENTIAL DERIVATIVE AT THE BOUNDARY FOR HOLOMORPHIC FUNCTION vol.29, pp.3, 2014, https://doi.org/10.4134/CKMS.2014.29.3.439
  7. CARATHÉODORY'S INEQUALITY ON THE BOUNDARY vol.22, pp.2, 2015, https://doi.org/10.7468/jksmeb.2015.22.2.169
  8. INEQUALITIES FOR THE ANGULAR DERIVATIVES OF CERTAIN CLASSES OF HOLOMORPHIC FUNCTIONS IN THE UNIT DISC vol.53, pp.2, 2016, https://doi.org/10.4134/BKMS.2016.53.2.325
  9. A SHARP CARATHÉODORY'S INEQUALITY ON THE BOUNDARY vol.31, pp.3, 2016, https://doi.org/10.4134/CKMS.c150194
  10. AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY vol.23, pp.1, 2016, https://doi.org/10.7468/jksmeb.2016.23.1.61
  11. On boundary analysis for derivative of driving point impedance functions and its circuit applications pp.1751-8598, 2018, https://doi.org/10.1049/iet-cds.2018.5123
  12. The Schwarz Lemma at the Boundary of the Egg Domain Bp1,p2 in ℂn vol.58, pp.02, 2015, https://doi.org/10.4153/CMB-2014-067-7
  13. Some remarks for a certain class of holomorphic functions at the boundary of the unit disc pp.1301-4048, 2019, https://doi.org/10.16984/saufenbilder.464294
  14. Schwarz lemma for driving point impedance functions and its circuit applications pp.00989886, 2019, https://doi.org/10.1002/cta.2616