SOME RESULTS ON THE SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS

Yıl 2022, Cilt: 3 Sayı: 1, 33 - 48, 30.06.2022

Bülent Nafi Örnek

https://doi.org/10.54559/jauist.1116695

Öz

The aim of this paper is to introduce the class of the analytic functions called and to investigate the various properties of the functions belonging this class. For the functions in this class, some inequalities related to the angular derivative have been obtained.

Anahtar Kelimeler

Jack’s lemma, Subordination Principle, Schwarz lemma.

Kaynakça

• Akyel. T. and Örnek, B. N. (2016). Sharpened forms of the Generalized Schwarz inequality on the boundary, Proc. Indian Acad. Sci. (Math. Sci.), 126(1), 69-78.
• Azeroğlu, T. A. and Örnek, B. N. (2013). A refined Schwarz inequality on the boundary, Complex Variab. Elliptic Equa., 58, 571-577.
• Boas, H. P. (2010). Julius and Julia: Mastering the Art of the Schwarz lemma, Amer. Math. Monthly, 117, 770-785.
• Dubinin, V. N. (2004). The Schwarz inequality on the boundary for functions regular in the disc, J. Math. Sci., 122, 3623-3629.
• Golusin G. M. (1996). Geometric Theory of Functions of Complex Variable [in Russian], 2nd edn., Moscow.
• Jack, I. S. (1971). Functions starlike and convex of order , J. London Math. Soc., 3, 469-474.
• Mateljevic, M. (2018). Rigidity of holomorphic mappings & Schwarz and Jack lemma, Researchgate.
• Mateljevic, M., Mutavdžć, N. and Örnek B. N. (2022), Estimates for some classes of holomorphic functions in the unit disc, Applicable Analysis and Discrete Mathematics, In press.
• Mercer, P. R. (2018). Boundary Schwarz inequalities arising from Rogosinski’s lemma, Journal of Classical Analysis, 12, 93-97.
• Mercer, P. R. (2018). An improved Schwarz Lemma at the boundary, Open Mathematics, 16, 1140-1144.
• Nunokawa, M., Sokól, J. and Tang, H. (2020). An application of Jack-Fukui-Sakaguchi lemma, Journal of Applie Analysis and Computation, 10, 25-31.
• Nunokawa, M. and Sokól, J. (2017). On a boundary property of analytic functions, J. Ineq. Appl., 298, 1-7.
• Mushtaq, S., Raza, M. and Sokól, J. (2021). Differential Subordination Related with Exponential Functions, Quaestiones Mathematicae, Online First Articles.
• Osserman, R. (2000). A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc., 128, 3513-3517.
• Örnek, B. N. (2016). The Carathéodory Inequality on the Boundary for Holomorphic Functions in the Unit Disc, Journal of Mathematical Physics, Analysis, Geometry, 12(4), 287-301.
• Örnek, B. N. and Düzenli, T. (2018). Boundary Analysis for the Derivative of Driving Point Impedance Functions, IEEE Transactions on Circuits and Systems II: Express Briefs, 65(9), 1149-1153.
• Örnek, B. N. and Düzenli, T. (2019). On Boundary Analysis for Derivative of Driving Point Impedance Functions and Its Circuit Applications, IET Circuits, Systems and Devices, 13(2), 145-152.
• Pommerenke, Ch. (1992). Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin.
• Unkelbach, H. (1938). Über die Randverzerrung bei konformer Abbildung, Math. Z., 43, 739-742.
• Wong, C. E. and Halim, S. A. (2015). Differential subordination properties for functions associated with the ssini’s oval, AIP Conference Proceedings 1682, 040004.