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Some remarks on the Subordination Principle for analytic functions concerned with Rogosinski's lemma
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In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Rogosinski's lemma, Subordination principle and Jack's lemma were used.
Abstract
In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Rogosinski's lemma, Subordination principle and Jack's lemma were used.
참고문헌 (15)
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- H. P. Boas, "Julius and Julia: Mastering the Art of the Schwarz lemma", Amer. Math. Monthly, 117, pp.770~785 (2010)
- V. N. Dubinin, "The Schwarz inequality on the boundary for functions regular in the disc", J. Math. Sci, 122, pp.3623~3629 (2004)
- G. M. Golusin, "Geometric Theory of Functions of Complex Variable" (1966)
- I. S. Jack, "Functions starlike and convex of order α", J. London Math. Soc, 3, pp.469~474 (1971)
- M. Mateljevic, "Rigidity of holomorphic mappings & Schwarz and Jack lemma", ~
- M. Mateljevic, "Note on Some Classes of Holomorphic Functions Related to Jack’s and Schwarz’s Lemma", ResearchGate, ~
- P. R. Mercer, "Boundary Schwarz inequalities arising from Rogosinski’s lemma", Journal of Clas-sical Analysis, 12, pp.93~97 (2018)
- P. R. Mercer, "An improved Schwarz Lemma at the boundary", Open Mathematics, 16, pp.1140~1144 (2018)
- R. Osserman, "A sharp Schwarz inequality on the boundary", Proc. Amer. Math. Soc, 128, pp.3513~3517 (2000)
- B. N. Ornek, "Bound Estimates for the Derivative of Driving Point Impedance Functions", Filomat, 32(18), pp.6211~6218 (2018)
- 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)
- Bulent Nafi Ornek, "Sharpened forms of the Schwarz lemma on the boundary", 대한수학회보, 50(6), pp.2053~2059 (2013), 대한수학회
- Ch. Pommerenke, "Boundary Behaviour of Conformal Maps" (1992), Springer-Verlag
관련 논문AI추천
APPLICATIONS OF SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMABÜLENT NAFI ÖRNEK, SELIN AYDINOĞLU한국수학교육학회 · 이론수학과 교직수학2020 · 제27권 제4호Applications 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 제2호Sharpened forms of analytic functions concerned with Hankel determinantBulent Nafi Ornek강원경기수학회 · 한국수학논문집2019 · 제27권 제4호Applications of the Schwarz Lemma and Jack’s Lemma for the Holomorphic FunctionsBatuhan Catal, Bulent Nafi Ornek경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호Estimates for analytic functions associated with Schwarz lemma on the boundaryAysan Kaynakkan, Bulent Nafi Ornek강원경기수학회 · 한국수학논문집2022 · 제30권 제2호
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