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APPLICATIONS OF SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA

SELIN AYDINOĞLU|BÜLENT NAFI ÖRNEK
한국수학교육학회|2020.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제27권 제4호|pp. 157-169|DOI https://doi.org/10.7468/jksmeb.2020.27.4.157

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참고문헌

키워드

Schwarz lemma on the boundaryanalytic functionRogosinski's lemmasubordinate principle .
주제분류수학

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 bound- ary point, the estimations below of the modulus of angular derivative have been obtained.

Abstract

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 bound- ary point, the estimations below of the modulus of angular derivative have been obtained.

참고문헌 (17)

  1. Tuğba AKYEL, "A SHARP SCHWARZ LEMMA AT THE BOUNDARY", 순수 및 응용수학, 22(3), pp.263~273 (2015), 한국수학교육학회
  2. T.A. Azeroglu, "A refined Schwarz inequality on the boundary", Complex Variables and Elliptic Equations, 58, pp.571~577 (2013)
  3. H.P. Boas, "Julius and Julia: Mastering the Art of the Schwarz lemma", Amer. Math. Monthly, 117, pp.770~785 (2010)
  4. V.N. Dubinin, "The Schwarz inequality on the boundary for functions regular in the disc", J. Math. Sci., 122, pp.3623~3629 (2004)
  5. G.M. Golusin, "Geometric Theory of Functions of Complex Variable" (1966)
  6. I.S. Jack, "Functions starlike and convex of order α", J. London Math. Soc., 3, pp.469~474 (1971)
  7. 정문자, "THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT", 순수 및 응용수학, 21(3), pp.219~227 (2014), 한국수학교육학회
  8. 정문자, "THE SCHWARZ LEMMA AND BOUNDARY FIXED POINTS", 순수 및 응용수학, 18(3), pp.275~284 (2011), 한국수학교육학회
  9. M. Mateljevic, "Rigidity of holomorphic mappings & Schwarz and Jack lemma"[DOI]
  10. P.R. Mercer, "Sharpened Versions of the Schwarz Lemma", J. Math. Anal. Appl., 205, pp.508~511 (1997)
  11. P.R. Mercer, "Boundary Schwarz inequalities arising from Rogosinski's lemma", Journal of Classical Analysis, 12, pp.93~97 (2018)
  12. P.R. Mercer, "An improved Schwarz Lemma at the boundary", Open Mathematics, 16, pp.1140~1144 (2018)
  13. R. Osserman, "A sharp Schwarz inequality on the boundary", Proc. Amer. Math. Soc., 128, pp.3513~3517 (2000)
  14. B.N. Ornek, "Bound Estimates for the Derivative of Driving Point Impedance Functions", Filomat, 32(18), pp.6211~6218 (2018)
  15. B.N. Ornek, "Boundary Analysis for the Derivative of Driving Point Impedance Functions", IEEE Transactions on Circuits and Systems II: Express Briefs, 65(9), pp.1149~1153 (2018)
  16. Bulent Nafi Ornek, "Sharpened forms of the Schwarz lemma on the boundary", 대한수학회보, 50(6), pp.2053~2059 (2013), 대한수학회
  17. Ch. Pommerenke, "Boundary Behaviour of Conformal Maps" (1992), Springer-Verlag

관련 논문AI추천

Some remarks on the Subordination Principle for analytic functions concerned with Rogosinski's lemmaTuğba Akyel강원경기수학회 · 한국수학논문집2021 · 제29권 제2호Applications of the Jack's Lemma for Analytic Functions concerned with Rogosinski's LemmaBülent Nafi ÖRNEK한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제3호Applications of Jack's lemma for certain subclasses of holomorphic functions on the unit discBatuhan Catal, Bulent Nafi Ornek대한수학회 · 대한수학회논문집2019 · 제34권 제2호Applications of the Schwarz Lemma and Jack’s Lemma for the Holomorphic FunctionsBatuhan Catal, Bulent Nafi Ornek경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit discB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회보2016 · 제53권 제2호AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARYBülent Nafi ÖRNEK, Tuğba AKYEL한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제1호

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