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Some Results Associated with the Hyperbolic Sine Function

Year 2024, Volume: 16 Issue: 1, 177 - 183, 30.06.2024
https://doi.org/10.47000/tjmcs.1452681

Abstract

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.

References

  • 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.
Year 2024, Volume: 16 Issue: 1, 177 - 183, 30.06.2024
https://doi.org/10.47000/tjmcs.1452681

Abstract

References

  • 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.
There are 15 citations in total.

Details

Primary Language English
Subjects Real and Complex Functions (Incl. Several Variables)
Journal Section Articles
Authors

Bülent Nafi Örnek 0000-0001-7109-230X

Süleyman Dirik 0000-0001-9093-1607

Mustafa Kandemir 0000-0002-3642-9699

Publication Date June 30, 2024
Submission Date March 14, 2024
Acceptance Date May 26, 2024
Published in Issue Year 2024 Volume: 16 Issue: 1

Cite

APA Örnek, 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
AMA Örnek BN, Dirik S, Kandemir M. Some Results Associated with the Hyperbolic Sine Function. TJMCS. June 2024;16(1):177-183. doi:10.47000/tjmcs.1452681
Chicago Örnek, Bülent Nafi, Süleyman Dirik, and Mustafa Kandemir. “Some Results Associated With the Hyperbolic Sine Function”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 177-83. https://doi.org/10.47000/tjmcs.1452681.
EndNote Örnek BN, Dirik S, Kandemir M (June 1, 2024) Some Results Associated with the Hyperbolic Sine Function. Turkish Journal of Mathematics and Computer Science 16 1 177–183.
IEEE B. N. Örnek, S. Dirik, and M. Kandemir, “Some Results Associated with the Hyperbolic Sine Function”, TJMCS, vol. 16, no. 1, pp. 177–183, 2024, doi: 10.47000/tjmcs.1452681.
ISNAD Örnek, Bülent Nafi et al. “Some Results Associated With the Hyperbolic Sine Function”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 177-183. https://doi.org/10.47000/tjmcs.1452681.
JAMA Örnek BN, Dirik S, Kandemir M. Some Results Associated with the Hyperbolic Sine Function. TJMCS. 2024;16:177–183.
MLA Örnek, Bülent Nafi et al. “Some Results Associated With the Hyperbolic Sine Function”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 177-83, doi:10.47000/tjmcs.1452681.
Vancouver Örnek BN, Dirik S, Kandemir M. Some Results Associated with the Hyperbolic Sine Function. TJMCS. 2024;16(1):177-83.