Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus
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A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral.
Keywords:
polynomial bounds / L’Hôpital’s rule of monotonicity / Jordan’s inequality / trigonometric functionsSource:
Symmetry, 2022, 14, 6Publisher:
- MDPI
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GraFarTY - JOUR AU - Stojiljković, Vuk AU - Radojević, Slobodan AU - Çetin, Eyüp AU - Šešum-Čavić, Vesna AU - Radenović, Stojan PY - 2022 UR - https://grafar.grf.bg.ac.rs/handle/123456789/3323 AB - A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral. PB - MDPI T2 - Symmetry T1 - Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus IS - 6 VL - 14 DO - 10.3390/sym14061260 ER -
@article{ author = "Stojiljković, Vuk and Radojević, Slobodan and Çetin, Eyüp and Šešum-Čavić, Vesna and Radenović, Stojan", year = "2022", abstract = "A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral.", publisher = "MDPI", journal = "Symmetry", title = "Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus", number = "6", volume = "14", doi = "10.3390/sym14061260" }
Stojiljković, V., Radojević, S., Çetin, E., Šešum-Čavić, V.,& Radenović, S.. (2022). Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus. in Symmetry MDPI., 14(6). https://doi.org/10.3390/sym14061260
Stojiljković V, Radojević S, Çetin E, Šešum-Čavić V, Radenović S. Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus. in Symmetry. 2022;14(6). doi:10.3390/sym14061260 .
Stojiljković, Vuk, Radojević, Slobodan, Çetin, Eyüp, Šešum-Čavić, Vesna, Radenović, Stojan, "Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus" in Symmetry, 14, no. 6 (2022), https://doi.org/10.3390/sym14061260 . .