In this paper, we provide a new simple proof of a double inequality of Masjed-Jamei type proved by L. Zhu [
Citation: Fen Wang. A new proof of a double inequality of Masjed-Jamei type[J]. AIMS Mathematics, 2024, 9(4): 8768-8775. doi: 10.3934/math.2024425
In this paper, we provide a new simple proof of a double inequality of Masjed-Jamei type proved by L. Zhu [
[1] | L. Zhu, New double inequality of Masjed-Jamei-type, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 117 (2023), 41. https://doi.org/10.1007/s13398-022-01375-6 doi: 10.1007/s13398-022-01375-6 |
[2] | M. Masjed-Jamei, A main inequality for several special functions, Comput. Math. Appl., 60 (2010), 1280–1289. https://doi.org/10.1016/j.camwa.2010.06.007 doi: 10.1016/j.camwa.2010.06.007 |
[3] | L. Zhu, B. Male$\breve{\rm{s}}$ević, Inequalities between the inverse hyperbolic tangent and the inverse sine and the analogue for corresponding functions, J. Inequal. Appl., 2019 (2019), 1–10. https://doi.org/10.1186/s13660-019-2046-2 doi: 10.1186/s13660-019-2046-2 |
[4] | L. Zhu, B. Male$\breve{\rm{s}}$ević, Natural approximation of Masjed-Jamei's inequality, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 114 (2020), 25. https://doi.org/10.1007/s13398-019-00735-z doi: 10.1007/s13398-019-00735-z |
[5] | C. P. Chen, B. Male$\breve{\rm{s}}$ević, Inequalities related to certain inverse trigonometric and inverse hyperbolic functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 114 (2020), 105. https://doi.org/10.1007/s13398-020-00836-0 doi: 10.1007/s13398-020-00836-0 |
[6] | C. Chesneau, , Y. J. Bagul, On a reverse trigonometric Masjed-Jamei inequality, Asia Pac. J. Math., 8 (2021), 1–5. https://doi.org/10.28924/APJM/8-13 doi: 10.28924/APJM/8-13 |
[7] | X. D. Chen, L. Nie, W. K. Huang, New inequalities between the inverse hyperbolic tangent and the analogue for corresponding functions, J. Inequal. Appl., 2020 (2020), 1–8. https://doi.org/10.1186/s13660-020-02396-8 doi: 10.1186/s13660-020-02396-8 |