Some New Improvements of Huygen's Inequality

Year 2023, Volume: 15 Issue: 1, 157 - 163, 30.06.2023

Seyran İbrahimov , Ahmad Issa

https://doi.org/10.47000/tjmcs.1167007

Abstract

First, some improvements of Young’s inequality are given in this article. Then, using these improve-
ments, stronger results were obtained from the Huygens inequality.

Keywords

Young inequality, hyperbolic functions, Huygen inequality

References

• Cajori, F., A History of Mathematics, American Mathematical Society, 1999.
• Hardy, G.H., Littlewood, J.E., P´olya, G., P´olya, G., Inequalities, Cambridge university press, 1952.
• Huygens, C., Oeuvres completes, publiees par la Societe hollandaise des science, Haga, 1940(1888), 1–20.
• Ibrahimov, S., Inequalities related to generalized hyperbolic functions and logarithmic mean, Romanian Mathematical Magazine, 2(2022), 1–8.
• Ibrahimov, S., Research proposal collection-2022, Romanian Mathematical Magazine, (2022), 1–107.
• Issa, A., Ibrahimov, S., New inequalities for hyperbolic Lucas functions, Journal of New Theory, 41(2022), 51–61.
• Lazarevic, I., Neke nejednakosti sa hiperbolickim funkcijama, Univerzitet u Beogradu. Publikacije Elektrotehnickog Fakulteta. Serija Matematikai Fizika, 170(1966), 41–48.
• Mitrinovic, D.S., Vasic, P.M., Analytic Inequalities, Berlin: Springer-verlag, 1. 1970.
• Nantomah, K., Cusa-Huygens, Wilker and Huygens type inequalities for generalized hyperbolic functions, Earthline Journal of Mathematical Sciences, 5(2)(2021), 277–289.
• Nantomah, K., Prempeh, E., Some inequalities for generalized hyperbolic functions, Moroccan Journal of Pure and Applied Analysis, 6(1)(2020), 76–92.
• Neuman, E., Sandor, J., On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities, Mathematical Inequalities and Applications, 13(4)(2010), 715–723