Browse > Article
http://dx.doi.org/10.7468/jksmeb.2022.29.1.113

ON A CLASS OF ANALYTIC FUNCTION RELATED TO SCHWARZ LEMMA  

Ornek, Bulent Nafi (Department of Computer Engineering, Amasya University)
Publication Information
The Pure and Applied Mathematics / v.29, no.1, 2022 , pp. 113-124 More about this Journal
Abstract
In this paper, we plan to introduce the class of the analytic functions called 𝒫 (b) and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient c2 in the expansion of f(z) = z+c2z2+… belonging to the given class will be estimated from above. Also, we estimate a modulus of the second angular derivative of f(z) function at the boundary point 𝛼 with f'(𝛼) = 1 - b, b ∈ ℂ, by taking into account their first nonzero two Maclaurin coefficients.
Keywords
analytic function; Schwarz lemma;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Mateljevic: Schwarz Lemma, and Distortion for Harmonic Functions Via Length and Area. Potential Analysis 53 (2020), 1165-1190. https://doi.org/10.1007/s11118-019-09802-x   DOI
2 G.M. Golusin: Geometric Theory of Functions of Complex Variable. [in Russian], 2nd edn., Moscow 1966.
3 P.R. Mercer: Boundary Schwarz inequalities arising from Rogosinski's lemma. Journal of Classical Analysis 12 (2018), 93-97. https://doi.org/10.7153/jca-2018-12-08   DOI
4 P.R. Mercer: An improved Schwarz Lemma at the boundary. Open Mathematics 16 (2018), 1140-1144. https://doi.org/10.1515/math-2018-0096   DOI
5 B.N. Ornek:Applications of the Jack's lemma for analytic functions concerned with Rogosinski's lemma. Journal of the Korean Society of Mathematical Education Series B: THE PURE AND APPLIED MATHEMATICS 28 (2021), 235-246. https://doi.org/10.4134/BKMS.2013.50.6.2053
6 V.N. Dubinin: The Schwarz inequality on the boundary for functions regular in the disc. J. Math. Sci. 122 (2004), 3623-3629. https://doi.org/10.1023/B:JOTH.0000035237.43977.39   DOI
7 M. Mateljevic, N. Mutavdzc & B.N. Ornek: Estimates for some classes of holomorphic functions in the unit disc. Applicable Analysis and Discrete Mathematics, https://doi.org/10.13140/RG.2.2.25744.15369, In press.   DOI
8 B.N. Ornek & T. Duzenli: On Boundary Analysis for Derivative of Driving Point Impedance Functions and Its Circuit Applications. IET Circuits, Systems and Devices, 13 (2019), no. 2, 145-152. https://dx.doi.org/10.1049/iet-cds.2018.5123   DOI
9 R. Osserman: A sharp Schwarz inequality on the boundary. Proc. Amer. Math. Soc. 128 (2000), 3513-3517. https://doi.org/10.1090/S0002-9939-00-05463-0   DOI
10 B.N. Ornek & T. Duzenli: Boundary Analysis for the Derivative of Driving Point Impedance Functions. IEEE Transactions on Circuits and Systems II: Express Briefs 65 (2018), no. 9, 1149-1153. https://doi.org/10.1109/TCSII.2018.2809539   DOI
11 Ch. Pommerenke: Boundary Behaviour of Conformal Maps. Springer-Verlag, Berlin. 1992.
12 H. Unkelbach: Uber die Randverzerrung bei konformer Abbildung. Math. Z. 43 (1938), 739-742. https://doi.org/10.1007/BF01181115   DOI
13 H.P. Boas: Julius and Julia: Mastering the Art of the Schwarz lemma. Amer. Math. Monthly 117 (2010), 770-785. https://doi.org/10.4169/000298910x52164   DOI
14 T. Akyel & B.N. Ornek: Some Remarks on Schwarz Lemma at the Boundary. Filomat, 31 (2017), no. 13, 4139-4151. https://doi.org/10.2298/FIL1713139A   DOI
15 T.A. Azeroglu & B.N. Ornek: A refined Schwarz inequality on the boundary. Complex Variab. Elliptic Equa. 58 (2013), 571-577. https://doi.org/10.1080 /17476933.2012.718338   DOI