On a Class of Analytic Function related to Schwarz Lemma
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In this paper, we plan to introduce the class of the analytic functions called $\mathcal{P}\left( b\right) $ and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient $c_{2}$ in the expansion of $f(z)=z+c_{2}z^{2}+...$ 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 $% \alpha $ with $f^{\prime }(\alpha )=1-b$, $b\in %TCIMACRO{\U{2102} }% %BeginExpansion \mathbb{C} %EndExpansion $, by taking into account their first nonzero two Maclaurin coefficients.
Abstract
In this paper, we plan to introduce the class of the analytic functions called $\mathcal{P}\left( b\right) $ and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient $c_{2}$ in the expansion of $f(z)=z+c_{2}z^{2}+...$ 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 $% \alpha $ with $f^{\prime }(\alpha )=1-b$, $b\in %TCIMACRO{\U{2102} }% %BeginExpansion \mathbb{C} %EndExpansion $, by taking into account their first nonzero two Maclaurin coefficients.
참고문헌 (15)
- Tuğba Akyel, "Some remarks on Schwarz lemma at the boundary", Filomat, 31(13), pp.4139~4151 (2017), National Library of Serbia[DOI]
- T. Aliyev Azeroǧlu, "A refined Schwarz inequality on the boundary", Complex Variables and Elliptic Equations, 58(4), pp.571~577 (2012), Informa UK Limited[DOI]
- H.P. Boas, "Mastering the Art of the Schwarz lemma", Amer. Math. Monthly, 117, pp.770~785 (2010)[DOI]
- V. N. Dubinin, "The Schwarz Inequality on the Boundary for Functions Regular in the Disk", Journal of Mathematical Sciences, 122(6), pp.3623~3629 (2004), Springer Science and Business Media LLC[DOI]
- G.M. Golusin, "Geometric Theory of Functions of Complex Variable" (1966)
- M. Mateljević, "Schwarz Lemma, and Distortion for Harmonic Functions Via Length and Area", Potential Analysis, 53(4), pp.1165~1190 (2020), Springer Science and Business Media LLC[DOI]
- M. Mateljević, "Applicable Analysis and Discrete Mathematics"
- Peter R. Mercer, "Boundary Schwarz inequalities arising from Rogosinski's lemma", Journal of Classical Analysis, (2), pp.93~97 (2018), Element d.o.o.[DOI]
- Peter R. Mercer, "An improved Schwarz Lemma at the boundary", Open Mathematics, 16(1), pp.1140~1144 (2018), Walter de Gruyter GmbH[DOI]
- Robert Osserman, "A sharp Schwarz inequality on the boundary", Proceedings of the American Mathematical Society, 128(12), pp.3513~3517 (2000), American Mathematical Society (AMS)[DOI]
- Bülent Nafi ÖRNEK, "Applications of the Jack's Lemma for Analytic Functions concerned with Rogosinski's Lemma", 순수 및 응용수학, 28(3), pp.235~246 (2021), 한국수학교육학회[DOI]
- Bulent Nafi 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), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
- Bülent Nafi Örnek, "On boundary analysis for derivative of driving point impedance functions and its circuit applications", IET Circuits, Devices & Systems, 13(2), pp.145~152 (2018), Institution of Engineering and Technology (IET)[DOI]
- Ch. Pommerenke, "Boundary Behaviour of Conformal Maps" (1992), Springer-Verlag
- Helmut Unkelbach, "Uber die Randverzerrung bei konformer Abbildung", Mathematische Zeitschrift, 43(1), pp.739~742 (1938), Springer Science and Business Media LLC[DOI]