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Applications of the Jack's Lemma for Analytic Functions concerned with Rogosinski's Lemma

Bülent Nafi ÖRNEK
한국수학교육학회|2021.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제28권 제3호|pp. 235-246|DOI https://doi.org/10.7468/jksmeb.2021.28.3.235

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참고문헌

키워드

Schwarz lemmaanalytic functionJulia-Wolff lemmaJack’s lemmaRogosinski’s lemma
주제분류수학

초록

In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered.The results of Rogosinski’s lemma and Jack’s lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.

Abstract

In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered.The results of Rogosinski’s lemma and Jack’s lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.

참고문헌 (16)

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  3. H.P. Boas, "Julius and Julia: Mastering the Art of the Schwarz lemma", Amer. Math. Monthly, 117, pp.770~785 (2010)
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  5. G.M. Golusin, "Geometric Theory of Functions of Complex Variable" (1966), Moscow
  6. I.S. Jack, "Functions starlike and convex of order", 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. M. Mateljevic, "Note on Some Classes of Holomorphic Functions Related to Jack's and Schwarz's Lemma", ~
  9. P.R. Mercer, "Sharpened Versions of the Schwarz Lemma", J. Math. Anal. Appl, 205, pp.508~511 (1997)
  10. P. R. Mercer, "Boundary Schwarz inequalities arising from Rogosinski's lemma", Journal of Classical Analysis, 12, pp.93~97 (2018)
  11. P. R. Mercer, "An improved Schwarz lemma at the boundary", Open Mathematics, 16, pp.1140~1144 (2018)
  12. R. Osserman, "A sharp Schwarz inequality on the boundary", Proc. Amer. Math. Soc, 128, pp.3513~3517 (2000)
  13. B.N. Ornek, "Bound Estimates for the Derivative of Driving Point Impedance Functions", Filomat, 32(18), pp.6211~6218 (2018)
  14. 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)
  15. Bulent Nafi Ornek, "Sharpened forms of the Schwarz lemma on the boundary", 대한수학회보, 50(6), pp.2053~2059 (2013), 대한수학회
  16. 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 SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMABÜLENT NAFI ÖRNEK, SELIN AYDINOĞLU한국수학교육학회 · 이론수학과 교직수학2020 · 제27권 제4호Applications 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 제3호Sharpened forms of analytic functions concerned with Hankel determinantBulent Nafi Ornek강원경기수학회 · 한국수학논문집2019 · 제27권 제4호Results associated with the Schwarz lemma on the boundaryBulent Nafi Ornek대한수학회 · 대한수학회논문집2023 · 제38권 제2호

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