Certain inequalities of Kober and Lazarevic type

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Authors

  • Department of Mathematics, K. K. M. College, Manwath 431505 ,IN
  • Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004 ,IN

DOI:

https://doi.org/10.18311/jims/2022/20737

Keywords:

Lazarevi´c inequality, Kober’s inequality, sharp bounds, exponential bounds, hyperbolic cosine

Abstract

In this work, the authors present new lower and upper bounds for cos x and cosh x, thus improving some generalized inequalities of Kober and Lazarevic type.

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Published

2022-01-27

How to Cite

Bagul, Y. J., & Panchal, S. K. (2022). Certain inequalities of Kober and Lazarevic type. The Journal of the Indian Mathematical Society, 89(1-2), 01–07. https://doi.org/10.18311/jims/2022/20737
Received 2018-04-01
Accepted 2021-09-13
Published 2022-01-27

 

References

G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Conformal Invariants, Inequalities and Quasiconformal Maps, John Wiley and Sons, New York, 1997.

Y. J. Bagul, On exponential bounds of hyperbolic cosine, Bull. International Math. Virtual Institute, 8(2)(2018), 365–367.

B. A. Bhayo and J. S´andor, On Jordan’s and Kober’s inequality, Acta Et Commentationes Universitatis tartuensis de Mathematica, 20(2)(2016), 111–116. DOI: https://doi.org/10.12697/ACUTM.2016.20.09

M. Bencze, S.-G. Li and S.-H. Wu, Sharpened versions of Mitrinovi´c-Adamovi´c, Lazarevi´c and Wilker’s inequalities for trigonometric and hyperbolic functions, J. Nonlinear Sci. Appl., 9 (2016), 2688–2696. DOI: https://doi.org/10.22436/jnsa.009.05.65

C. P. Chen, F. Qi and J. W. Zhao, Three inequalities involving hyperbolically trigonometric functions, RGMIA Res. Rep. Coll., 6(3)(2003), Art. 4, 437–443.

Y. Chu, Y. LV and G. Wang, A note on Jordan type inequalities for hyperbolic functions, Appl. Math. Lett., 25(2012), 505–508. DOI: https://doi.org/10.1016/j.aml.2011.09.046

Y. Chu, G. Wang and X. Zhang, Extensions and sharpenings of Jordan’s and Kober’s inequalities, J. Inequal. Pure. Appl. Math., 7(2)(2006), Article 63, 3 pages.

R. Kl´en, M. Visuri and M. Vuorinen, On Jordan type inequalities for hyperbolic functions, J. Inequal. and Appl., (2010), Art. ID 362548, 14 pages. DOI: https://doi.org/10.1155/2010/362548

H. Kober, Approximation by integral functions in the complex domain, Trans. Amer. Math. Soc., 56(1)(1944), 7–31. DOI: https://doi.org/10.2307/1990275

I. Lazarevi´c, Neke nejednakosti sa hiperbolickim funkcijama, Univerzitet u Beogradu. Publikacije Elektrotechni?ckog Fakulteta. Serija Matematika i Fizika, 170 (1966), 41–48.

D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, Berlin, 1970. DOI: https://doi.org/10.1007/978-3-642-99970-3

R. Redheffer, Problem 5642, Amer. Math. Monthly, 76 (1969), 422. DOI: https://doi.org/10.2307/2316453

J. S´andor, On new refinements of Kober’s and Jordan’s trigonometric inequalities, Notes Number Theory and Discrete Math., 19(1)(2013), 73–83.

J. S´andor, Refinements of the Mitrinovi´c - Adamovi´c inequality, with application, Notes Number Theory and Discrete Math., 23(1)(2017), 4–6.

L. Zhu and J. Sun, Six new Redheffer-type inequalities for circular and hyperbolic functions, Comput. Math. Appl., 56(2)(2008), 522–529. DOI: https://doi.org/10.1016/j.camwa.2008.01.012