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http://dx.doi.org/10.7468/jksmeb.2020.27.4.157

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

Aydinoglu, Selin (Department of Computer Engineering, Amasya University)
Ornek, Bulent Nafi (Department of Computer Engineering, Maltepe University)
Publication Information
The Pure and Applied Mathematics / v.27, no.4, 2020 , pp. 157-169 More about this Journal
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 boundary point, the estimations below of the modulus of angular derivative have been obtained.
Keywords
Schwarz lemma on the boundary; Rogosinski's lemma; analytic function; subordinate principle;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 T. Akyel & B.N. Ornek: A Sharp Schwarz lemma at the boundary. J. Korean Soc. Math. Ser. B: Pure Appl. Math. 22 (2015), no. 3, 263-273.
2 T.A. Azero glu & B.N. Ornek: A refined Schwarz inequality on the boundary. Complex Variables and Elliptic Equations 58 (2013), 571-577.   DOI
3 H.P. Boas: Julius and Julia: Mastering the Art of the Schwarz lemma. Amer. Math. Monthly 117 (2010), 770-785.   DOI
4 V.N. Dubinin: The Schwarz inequality on the boundary for functions regular in the disc. J. Math. Sci. 122 (2004), 3623-3629.   DOI
5 G.M. Golusin: Geometric Theory of Functions of Complex Variable [in Russian]. 2nd edn., Moscow 1966.
6 I.S. Jack: Functions starlike and convex of order α. J. London Math. Soc. 3 (1971), 469-474.   DOI
7 M. Jeong: The Schwarz lemma and its applications at a boundary point. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 21 (2014), 275-284.
8 M. Mateljevic: Rigidity of holomorphic mappings & Schwarz and Jack lemma. DOI:10.13140/RG.2.2.34140.90249, In press.   DOI
9 P.R. Mercer: Sharpened Versions of the Schwarz Lemma. J. Math. Anal. Appl. 205 (1997), 508-511.   DOI
10 P.R. Mercer: Boundary Schwarz inequalities arising from Rogosinski's lemma. Journal of Classical Analysis 12 (2018), 93-97.   DOI
11 P.R. Mercer: An improved Schwarz Lemma at the boundary. Open Mathematics 16 (2018), 1140-1144.   DOI
12 R. Osserman: A sharp Schwarz inequality on the boundary. Proc. Amer. Math. Soc. 128 (2000) 3513-3517.   DOI
13 B.N. Ornek & T. Duzenli: Bound Estimates for the Derivative of Driving Point Impedance Functions. Filomat 32 (2018), no. 18, 6211-6218..   DOI
14 B.N. Ornek & T. Dzenli: 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.   DOI
15 B.N. Ornek: Sharpened forms of the Schwarz lemma on the boundary. Bull. Korean Math. Soc. 50 (2013), no. 6, 2053-2059.   DOI
16 Ch. Pommerenke: Boundary Behaviour of Conformal Maps. Springer-Verlag, Berlin. 1992.
17 M. Jeong: The Schwarz lemma and boundary fixed points. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 18 (2011), 219-227.