Some Results Associated with the Hyperbolic Sine Function

Yıl 2024, Cilt: 16 Sayı: 1, 177 – 183, 30.06.2024

Bülent Nafi Örnek Süleyman Dirik Mustafa Kandemir

https://doi.org/10.47000/tjmcs.1452681

Öz

In this paper, we examine several characteristics of analytical functions related to the hyperbolic sine
function and analyze the behavior of the hyperbolic sine function inside and at the boundary of the unit disk.

Anahtar Kelimeler

Jack’s lemma, Analytic function, Schwarz lemma.

Kaynakça

• Akyel, T., Estimates for λ-spirallike function of complex order on the boundary, Ukrainian Math.J., 74(1)(2022), 1–14.
• Azeroğlu, T.A., Örnek, B.N., A refined Schwarz inequality on the boundary, Complex Variables and Elliptic Equations, 58(2013), 571–577.
• Boas, H.P., Julius and Julia: Mastering the art of the Schwarz lemma, Amer. Math. Monthly, 117(2010), 770–785.
• Dubinin, V.N., The Schwarz inequality on the boundary for functions regular in the disc, J. Math. Sci., 122(2004), 3623–3629.
• Golusin, G.M., Geometric Theory of Functions of Complex Variable [in Russian], 2nd edn., Moscow, 1966.
• Jack, I.S., Functions starlike and convex of order α, J. London Math. Soc., 3(1971), 469–474.
• Kumar, S.S., Khan, M.G., Ahmad, B. et al., A class of analytic functions associated with sine hyperbolic functions, The Journal of Analysis, (2024).
• Mateljevic, M., Mutavdzc, N., Örnek, B.N., Note on some classes of holomorphic functions related to Jack’s and Schwarz’s lemma, Appl. Anal. Discrete Math., 16 (2022), 111–131.
• Mercer, P.R., Boundary Schwarz inequalities arising from Rogosinski’s lemma, J. Class. Anal., 12(2018), 93–97.
• Mercer, P.R., An improved Schwarz Lemma at the boundary, Open Math., 16(2018), 1140–1144.
• Osserman, R., A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc., 128(2000), 3513–3517.
• Örnek, B.N., Düzenli, T., Boundary analysis for the derivative of driving point impedance functions, IEEE Transactions on Circuits and Systems II: Express Briefs, 65(9)(2018), 1149–1153.
• Örnek, B.N., Sharpened forms of the Schwarz lemma on the boundary, Bull. Korean Math. Soc., 50(6)(2013), 2053–2059.
• Pommerenke, Ch., Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.
• Unkelbach, H., Über die randverzerrung bei konformer abbildung, Math. Z., 43(1938), 739–742.

Yıl 2024, Cilt: 16 Sayı: 1, 177 – 183, 30.06.2024

Bülent Nafi Örnek Süleyman Dirik Mustafa Kandemir

https://doi.org/10.47000/tjmcs.1452681

Öz

Kaynakça

• Akyel, T., Estimates for λ-spirallike function of complex order on the boundary, Ukrainian Math.J., 74(1)(2022), 1–14.
• Azeroğlu, T.A., Örnek, B.N., A refined Schwarz inequality on the boundary, Complex Variables and Elliptic Equations, 58(2013), 571–577.
• Boas, H.P., Julius and Julia: Mastering the art of the Schwarz lemma, Amer. Math. Monthly, 117(2010), 770–785.
• Dubinin, V.N., The Schwarz inequality on the boundary for functions regular in the disc, J. Math. Sci., 122(2004), 3623–3629.
• Golusin, G.M., Geometric Theory of Functions of Complex Variable [in Russian], 2nd edn., Moscow, 1966.
• Jack, I.S., Functions starlike and convex of order α, J. London Math. Soc., 3(1971), 469–474.
• Kumar, S.S., Khan, M.G., Ahmad, B. et al., A class of analytic functions associated with sine hyperbolic functions, The Journal of Analysis, (2024).
• Mateljevic, M., Mutavdzc, N., Örnek, B.N., Note on some classes of holomorphic functions related to Jack’s and Schwarz’s lemma, Appl. Anal. Discrete Math., 16 (2022), 111–131.
• Mercer, P.R., Boundary Schwarz inequalities arising from Rogosinski’s lemma, J. Class. Anal., 12(2018), 93–97.
• Mercer, P.R., An improved Schwarz Lemma at the boundary, Open Math., 16(2018), 1140–1144.
• Osserman, R., A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc., 128(2000), 3513–3517.
• Örnek, B.N., Düzenli, T., Boundary analysis for the derivative of driving point impedance functions, IEEE Transactions on Circuits and Systems II: Express Briefs, 65(9)(2018), 1149–1153.
• Örnek, B.N., Sharpened forms of the Schwarz lemma on the boundary, Bull. Korean Math. Soc., 50(6)(2013), 2053–2059.
• Pommerenke, Ch., Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.
• Unkelbach, H., Über die randverzerrung bei konformer abbildung, Math. Z., 43(1938), 739–742.

Toplam 15 adet kaynakça vardır.

Ayrıntılar

Kaynak Göster

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