Some Results Associated with the Hyperbolic Sine Function

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

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

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

Birincil Dil İngilizce
Konular Reel ve Kompleks Fonksiyonlar
BölümMakaleler
Yazarlar

Bülent Nafi Örnek Amasya Üniversitesi 0000-0001-7109-230X Türkiye

Süleyman Dirik AMASYA UNIVERSITY 0000-0001-9093-1607 Türkiye

Mustafa Kandemir AMASYA UNIVERSITY 0000-0002-3642-9699 Türkiye

Yayımlanma Tarihi30 Haziran 2024
Gönderilme Tarihi14 Mart 2024
Kabul Tarihi26 Mayıs 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 16 Sayı: 1

Kaynak Göster

APAÖrnek, B. N., Dirik, S., & Kandemir, M. (2024). Some Results Associated with the Hyperbolic Sine Function. Turkish Journal of Mathematics and Computer Science, 16(1), 177-183. https://doi.org/10.47000/tjmcs.1452681
AMAÖrnek BN, Dirik S, Kandemir M. Some Results Associated with the Hyperbolic Sine Function. TJMCS. Haziran 2024;16(1):177-183. doi:10.47000/tjmcs.1452681
ChicagoÖrnek, Bülent Nafi, Süleyman Dirik, ve Mustafa Kandemir. “Some Results Associated With the Hyperbolic Sine Function”. Turkish Journal of Mathematics and Computer Science 16, sy. 1 (Haziran 2024): 177-83. https://doi.org/10.47000/tjmcs.1452681.
EndNoteÖrnek BN, Dirik S, Kandemir M (01 Haziran 2024) Some Results Associated with the Hyperbolic Sine Function. Turkish Journal of Mathematics and Computer Science 16 1 177–183.
IEEEB. N. Örnek, S. Dirik, ve M. Kandemir, “Some Results Associated with the Hyperbolic Sine Function”, TJMCS, c. 16, sy. 1, ss. 177–183, 2024, doi: 10.47000/tjmcs.1452681.
ISNADÖrnek, Bülent Nafi vd. “Some Results Associated With the Hyperbolic Sine Function”. Turkish Journal of Mathematics and Computer Science 16/1 (Haziran 2024), 177-183. https://doi.org/10.47000/tjmcs.1452681.
JAMAÖrnek BN, Dirik S, Kandemir M. Some Results Associated with the Hyperbolic Sine Function. TJMCS. 2024;16:177–183.
MLAÖrnek, Bülent Nafi vd. “Some Results Associated With the Hyperbolic Sine Function”. Turkish Journal of Mathematics and Computer Science, c. 16, sy. 1, 2024, ss. 177-83, doi:10.47000/tjmcs.1452681.
VancouverÖrnek BN, Dirik S, Kandemir M. Some Results Associated with the Hyperbolic Sine Function. TJMCS. 2024;16(1):177-83.

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