Inequalities Related to Some Trigonometric and Hyperbolic Functions

Authors

  • Amrut Nirwal  School of Mathematical Sciences, SRTM University, Nanded, Gujarat, India
  • Rupali Shinde  School of Mathematical Sciences, SRTM University, Nanded, Gujarat, India

DOI:

https://doi.org/10.32628/IJSRST523103211

Keywords:

Bernoulli's numbers; Inequalities of Trigonometric functions

Abstract

In current paper we are elaborated few Trigonometric and Hyperbolic inequalities using well known Bernoulli’s Number and Polynomial of trigonometric and hyperbolic functions.

References

  1. Abramowitz, Milton, and Irene A. Stegun, eds. Handbook of mathematical functions with formulas, graphs, and mathematical tables. Vol. 55. US Government printing office, 1964.
  2. Group of Compilation. ”Handbook of Mathematics”,Peoples’ Education Press, Beijing, China, (1979).
  3. Heikkala, V., Vamanamurthy, M. K., and Vuorinen, M. (2009). Generalized elliptic integrals. Computational Methods and Function Theory, 9(1), 75-109.
  4. Zhu, L. (2020). New bounds for the ratio of two adjacent even-indexed Bernoulli numbers. Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matem´aticas, 114(2), 1-13.
  5. Yang, Z. H., and Tian, J. F. (2020). Sharp bounds for the ratio of two zeta functions. Journal of Computational and Applied Mathematics, 364, 112359
  6. Qi, F. (2019). A double inequality for the ratio of two non-zero neighbouring Bernoulli numbers. Journal of Computational and Applied Mathematics, 351, 1-5
  7. Li, J. L. (2006). An identity related to Jordan’s inequality. International Journal of Mathematics and Mathematical Sciences, 2006.
  8. Kuang, Ji-Chang. ”Applied Inequalities (Changyong Budengshi).” (1993): 584
  9. Yang, Z. H., Chu, Y. M., and Wang, M. K. (2015). Monotonicity criterion for the quotient of power series with applications. Journal of Mathematical Analysis and Applications, 428(1), 587-604
  10. Jeffrey, A., and Dai, H. H. (2008). Handbook of mathematical formulas and integrals. Elsevier.
  11. Anderson, G., Vamanamurthy, M., and Vuorinen, M. (2006). Monotonicity rules in calculus. The American Mathematical Monthly, 113(9), 805-816.
  12. Alzer, H., and Qiu, S. L. (2003). Inequalities for means in two variables. Archiv der Mathematik, 80(2), 201-215.
  13. Ponnusamy, S., and Vuorinen, M. (1997). Asymptotic expansions and inequalities for hypergeometric function. Mathematika, 44(2), 278-301.
  14. Chen, C. P., and Cheung, W. S. (2011). Sharp Cusa and Becker-Stark inequalities. Journal of Inequalities and Applications, 2011(1), 1-6.
  15. Mortici, C. (2011). The natural approach of Wilker-Cusa-Huygens inequalities. Math. Inequal. Appl, 14(3), 535-541
  16. Neuman, E., and Sandor, J. (2010). On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities. Math. Inequal. Appl, 13(4), 715-723
  17. S´andor, J. (2013). Sharp Cusa-Huygens and related inequalities. Notes on number theory and discrete mathematics, 19(1), 50-54.

International Journal of Scientific Research in Science and Technology

Downloads

Published

2023-07-30

Issue

Volume 10, Issue 4, July-August-2023

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Amrut Nirwal, Rupali Shinde "Inequalities Related to Some Trigonometric and Hyperbolic Functions" International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011,Volume 10, Issue 4, pp.60-66, July-August-2023. Available at doi : https://doi.org/10.32628/IJSRST523103211