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A SHARP SCHWARZ LEMMA AT THE BOUNDARY

Bülent Nafi ÖRNEK|Tuğba AKYEL
한국수학교육학회|2015.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제22권 제3호|pp. 263-273

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키워드

Schwarz lemma on the boundaryAngular limit and derivativeJulia–Wolff–LemmaHolomorphic function
주제분류수학

초록

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z)=a+c_{p}z^{p}+c_{p+1}z^{p+1}+... defined in the unit disc satisfying |f(z)-1|<1, where 0 < a < 2, we estimate a module of angular

Abstract

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z)=a+c_{p}z^{p}+c_{p+1}z^{p+1}+... defined in the unit disc satisfying |f(z)-1|<1, where 0 < a < 2, we estimate a module of angular

참고문헌 (14)

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  2. D. Chelst, "A generalized Schwarz lemma at the boundary", Proc. Amer. Math. Soc, 129(11), pp.3275~3278 (2001)
  3. V.N. Dubinin, "The Schwarz inequality on the boundary for functions regular in the disc", J. Math. Sci, 122(6), pp.3623~3629 (2004)
  4. V.N. Dubinin, "Bounded holomorphic functions covering no concentric circles", Zap. Nauchn. Sem. POMI, 429, pp.34~43 (2015)
  5. G.M. Golusin, "Geometric Theory of Functions of Complex Variable" (1966)
  6. 정문자, "THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT", 순수 및 응용수학, 21(3), pp.219~227 (2014), 한국수학교육학회
  7. 정문자, "THE SCHWARZ LEMMA AND BOUNDARY FIXED POINTS", 순수 및 응용수학, 18(3), pp.275~284 (2011), 한국수학교육학회
  8. D.M. Burns, "Rigidity of holomorphic mappings and a new Schwarz Lemma at the boundary", J. Amer. Math. Soc, 7, pp.661~676 (1994)
  9. X. Tang, "The Schwarz Lemma at the Boundary of the Egg Domain Bp1;p2in Cn", Canad. Math. Bull, 58(2), pp.381~392 (2015)
  10. X. Tang, "Schwarz lemma at the boundary of the unit polydisk in Cn", Sci. China Math, 58, pp.1~14 (2015)
  11. R. Osserman, "A sharp Schwarz inequality on the boundary", Proc. Amer. Math. Soc, 128, pp.3513~3517 (2000)
  12. T. Aliyev Azeroglu, "A refined Schwarz inequality on the boundary", Complex Variables and Elliptic Equations, 58(4), pp.571~577 (2013)
  13. Bulent Nafi Ornek, "Sharpened forms of the Schwarz lemma on the boundary", 대한수학회보, 50(6), pp.2053~2059 (2013), 대한수학회
  14. Ch. Pommerenke, "Boundary Behaviour of Conformal Maps" (1992), Springer-Verlag

관련 논문AI추천

AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARYBülent Nafi ÖRNEK, Tuğba AKYEL한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제1호Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit discB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회보2016 · 제53권 제2호A sharp Carath\'{e}odory's inequality on the boundaryB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회논문집2016 · 제31권 제3호Sharpened forms of the Schwarz lemma on the boundaryBulent Nafi Ornek대한수학회 · 대한수학회보2013 · 제50권 제6호THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT정문자한국수학교육학회 · 이론수학과 교직수학2014 · 제21권 제3호On bounds for the derivative of analytic functions at the boundaryBulent Nafi Ornek, Tugba Akyel강원경기수학회 · 한국수학논문집2021 · 제29권 제4호

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