Dergiler / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 4

Remarks on inequalities for the tangent function

Sayfa
499–506
Yayın Tarihi
2022-10-18
DOI
—
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Moreover, the authors propose a sharp double inequality as a conjecture.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In the paper, the authors analyze and compare two double inequali- ties for bounding the tangent function, reorganize the proof in C.-P.
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Temel Bulgular & Veri:Math. 34 (4), 351–355, 2003) by using the usual definition of Bernoulli numbers, and correct some errors on page 6, (1.29) and (1.30) of F.
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Sonuç & Katkı:Moreover, the authors propose a sharp double inequality as a conjecture.
🔬Tür:Araştırma Makalesi
📍Kapsam:2003 Verileri
⚙️Değişkenler:Alan Parametreleri

Abstract

In the paper, the authors analyze and compare two double inequali- ties for bounding the tangent function, reorganize the proof in C.-P. Chen and F. Qi (A double inequality for remainder of power series of tangent function, Tamkang J. Math. 34 (4), 351–355, 2003) by using the usual definition of Bernoulli numbers, and correct some errors on page 6, (1.29) and (1.30) of F. Qi, D. -W. Niu, and B. -N. Guo (Re- finements, generalizations, and applications of Jordan’s inequality and related problems, J. Inequal. Appl. 2009 (2009), Article ID 271923, 52 pages, 2009). Moreover, the authors propose a sharp double inequality as a conjecture.

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Bu Makaleye Atıf Yap

LUO, Q. M., GUO, B. N., QI, F., ZHAO, J. L. (2022). Remarks on inequalities for the tangent function. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 4, 499–506. https://ajindex.com/articles/530518

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Kaynakça (13)

  1. Abramowitz, M. and Stegun, I.A. (Eds) Handbook of Mathematical Functions with Formu- las, Graphs, and Mathematical Tables (National Bureau of Standards, Applied Mathematics Series 55, 9th printing, Washington, 1970)
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  3. Becker, M. and Strak, E. L. On a hierarchy of polynomial inequalities for tan x, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 602-633, 133–138, 1978
  4. Chen, C. -P. and Qi, F. A double inequality for remainder of power series of tangent function, Tamkang J. Math. 34 (4), 351–355, 2003; Available online at
  5. Guo, B. -N. and Qi, F. A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 72 (2), 21–30, 2010
  6. Guo, B.-N. and Qi, F. Sharpening and generalizations of Carlson’s inequality for the arc cosine function, Hacet. J. Math. Stat. 39 (3), 403–409, 2010
  7. Kuang, J. -C. Ch´angy`ong B`udˇengsh`ı (Applied Inequalities), 3rd ed. (Shandong Science and Technology Press, Ji’nan City, Shandong Province, China, 2004). (in Chinese
  8. Mitrinovi´c, D. S. Analytic Inequalities (Springer-Verlag, New York, Heidelberg, Berlin, 1970)
  9. Qi, F. and Guo, B. -N. Sharpening and generalizations of Shafer’s inequality for the arc sine function, Integral Transforms Spec. Funct. 23 (2), 129–134, 2012; Available online at
  10. Qi, F., Niu, D. -W. and Guo, B. -N. Refinements, generalizations, and applications of Jor- dan’s inequality and related problems, J. Inequal. Appl. 2009 (2009), Article ID 271923, 52 pages, 2009; Available online at
  11. Qi, F., Zhang, S. -Q. and Guo, B. -N. Sharpening and generalizations of Shafer’s inequality for the arc tangent function, J. Inequal. Appl. 2009 (2009), Article ID 930294, 9 pages, 2009; Available online at
  12. Steckin, S.B. Some remarks on trigonmetric polynomials, Uspehi Mat. Nauk. (N.S.) 10 1 (63), 159–166, 1955. (in Russian
  13. Zhao, J. -L., Wei, C. -F., Guo, B. -N. and Qi, F. Sharpening and generalizations of Carlson’s double inequality for the arc cosine function, Hacet. J. Math. Stat. 41 (2), 201–209, 2012. [14]