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Optimal Inequality in the One-Parameter Arithmetic and Harmonic Means

DOI: 10.4236/oalib.1106586, PP. 1-8

Subject Areas: Mathematical Analysis

Keywords: One-Parameter, Arithmetic, Harmonic Means

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Abstract

This research work considers the inequalities: (Ieq). The researchers attempt to find an answer as to what are the best possible parameters α,β that (Ieq) can be hold? The main tool is the optimization of some suitable functions that we seek to find out.

Cite this paper

Mokhtar, M. E. M. O. E. and Alharbi, H. (2020). Optimal Inequality in the One-Parameter Arithmetic and Harmonic Means. Open Access Library Journal, 7, e6586. doi: http://dx.doi.org/10.4236/oalib.1106586.

References

[1]  Bullen, P.S., Mitrinovic, D.S. and Vasic, M. (2013) Means and Their Inequalities, Vol. 31, Springer Science & Business Media, Berlin.
[2]  Ostasiewicz, S. and Ostasiewicz, W. (2000) Means and Their Applications. Annals of Operations Research, 97, 337-355. https://doi.org/10.1023/A:1018932425645
[3]  Long, B.Y., Li, Y.M. and Chu, Y.M. (2012) Optimal Inequalities between Generalized Logarithmic, Identric and Power Means. International Journal of Pure and Applied Mathematics, 80, 41-51.
[4]  Xia, W-F. and Chu, Y.-M. (2010) Optimal Inequalities Related to the Logarithmic, Identric, Arithmetic and Harmonic Means. Rev. Anal. Numer. Theor. Approx., 39, 176-183.
[5]  Chen, J.-J., Lei, J.-J. and Long, B.-Y. (2017) Optimal Bounds for Neuman-Sandor Means in Term of the Convex Combination of the Logarithmic and the Second Seiffert Means. Journal of Inequalities and Applications, No. 1, 251. https://doi.org/10.1186/s13660-017-1516-7
[6]  Newman, E. and Sandor, J. (2003) On the Schwab-Borcharrdt Means. Math. Pannon, 14, 253-266.
[7]  Seiffert, S., Jungk, J.K.A. and Claassen, N. (1995) Observed and Calculated Potassium Uptake by Maize as Affected by Soil Water Content and Bulk Density. Agronomy Journal, 87, 1070-1077. https://doi.org/10.2134/agronj1995.00021962008700060007x
[8]  Xu, H.-Z., Chu, Y.-M. and Qian, W.-M. (2018) Sharp Bounds for the Sandor-Yang Means in Terms of Arithmetic and Contra-Harmonic Means. Journal of Inequalities and Applications, No. 1, 127. https://doi.org/10.1186/s13660-018-1719-6
[9]  Yang, Y.Y. and Qian, W.M. (2016) Two Optimal Inequalities Related to the Sandor-Yang Mean and One-Parameter Mean. Communications in Mathematical Research, 32, 352-358.
[10]  Yang, Z.-H., Jiang, Y.-L., Song, Y.-Q. and Chu, Y.-M. (2014) Sharp Inequalities for Trigonometric Functions. In: Abstract and Applied Analysis, Vol. 2014. Hindawi. https://doi.org/10.1155/2014/601839
[11]  Chu, Y.-M. and Hou, S.-W. (2012) Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean. In: Abstract and Applied Analysis, Vol. 2012, Hindawi. https://doi.org/10.1186/1029-242X-2012-11 Jiang, W.-D. and Qi, F. (2015) Sharp Bounds for the Neuman-Sandor Mean in Term of the Power and Contraharmonic Means. Cogent Mathematics, 2, 995951. https://doi.org/10.1080/23311835.2014.995951

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