Logarithms are indispensable in the revision of mathematics which are basic components tools in the theory of mathematical analysis. Logarithms have playing acute fundamental role in the study of the properties of power and arithmetic means as well as inequalities of Logarithms with their bound. This paper shows the properties of logarithms mean, power mean, arithmetic mean, Harmonic mean, geometric mean and later we use Minkowski’s inequality and Hölder’s inequality to establish the modified means. In the paper, we obtained the generalization of power mean, logarithms mean, arithmetic mean, Harmonic mean and geometric mean. The methodology adopted are Minkowski’s inequality and Hölder’s inequality to establish some means of order α of two distincts. These inequalities further generalize some existing results. This research work also demonstrated the importance of the Minkowski’s inequality and Hölder’s inequality over existing arithmetic mean, Harmonic mean and geometric mean and further extend the generalization to weighted logarithms mean. Hence, this article distinguished some present results on power mean, logarithms means and acquired more robust means by engaging modified Minkowski’s inequality and Hölder’s inequality with some ordinary theorems. The modified Minkowski’s inequality on power and logarithms mean further extends the generalized weighted logarithms mean of order α of two distincts.
Published in | Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 2) |
DOI | 10.11648/j.sjams.20221002.12 |
Page(s) | 22-27 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2022. Published by Science Publishing Group |
Extension of Logarithms Mean, Power Mean, Arithmetic Mean, Geometric Mean, Harmonic Mean, Minkowski’s Inequality and Hölder’s Inequality
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APA Style
Yisa Anthonio, Abimbola Abolarinwa, Abdullai Abdurasid, Kamal Rauf, Michael Adeniyi, et al. (2022). Extension of Power Mean and Logarithms Mean. Science Journal of Applied Mathematics and Statistics, 10(2), 22-27. https://doi.org/10.11648/j.sjams.20221002.12
ACS Style
Yisa Anthonio; Abimbola Abolarinwa; Abdullai Abdurasid; Kamal Rauf; Michael Adeniyi, et al. Extension of Power Mean and Logarithms Mean. Sci. J. Appl. Math. Stat. 2022, 10(2), 22-27. doi: 10.11648/j.sjams.20221002.12
@article{10.11648/j.sjams.20221002.12, author = {Yisa Anthonio and Abimbola Abolarinwa and Abdullai Abdurasid and Kamal Rauf and Michael Adeniyi and Adeyinka Ogunsanya and Christian Iluno}, title = {Extension of Power Mean and Logarithms Mean}, journal = {Science Journal of Applied Mathematics and Statistics}, volume = {10}, number = {2}, pages = {22-27}, doi = {10.11648/j.sjams.20221002.12}, url = {https://doi.org/10.11648/j.sjams.20221002.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221002.12}, abstract = {Logarithms are indispensable in the revision of mathematics which are basic components tools in the theory of mathematical analysis. Logarithms have playing acute fundamental role in the study of the properties of power and arithmetic means as well as inequalities of Logarithms with their bound. This paper shows the properties of logarithms mean, power mean, arithmetic mean, Harmonic mean, geometric mean and later we use Minkowski’s inequality and Hölder’s inequality to establish the modified means. In the paper, we obtained the generalization of power mean, logarithms mean, arithmetic mean, Harmonic mean and geometric mean. The methodology adopted are Minkowski’s inequality and Hölder’s inequality to establish some means of order α of two distincts. These inequalities further generalize some existing results. This research work also demonstrated the importance of the Minkowski’s inequality and Hölder’s inequality over existing arithmetic mean, Harmonic mean and geometric mean and further extend the generalization to weighted logarithms mean. Hence, this article distinguished some present results on power mean, logarithms means and acquired more robust means by engaging modified Minkowski’s inequality and Hölder’s inequality with some ordinary theorems. The modified Minkowski’s inequality on power and logarithms mean further extends the generalized weighted logarithms mean of order α of two distincts.}, year = {2022} }
TY - JOUR T1 - Extension of Power Mean and Logarithms Mean AU - Yisa Anthonio AU - Abimbola Abolarinwa AU - Abdullai Abdurasid AU - Kamal Rauf AU - Michael Adeniyi AU - Adeyinka Ogunsanya AU - Christian Iluno Y1 - 2022/04/20 PY - 2022 N1 - https://doi.org/10.11648/j.sjams.20221002.12 DO - 10.11648/j.sjams.20221002.12 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 22 EP - 27 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20221002.12 AB - Logarithms are indispensable in the revision of mathematics which are basic components tools in the theory of mathematical analysis. Logarithms have playing acute fundamental role in the study of the properties of power and arithmetic means as well as inequalities of Logarithms with their bound. This paper shows the properties of logarithms mean, power mean, arithmetic mean, Harmonic mean, geometric mean and later we use Minkowski’s inequality and Hölder’s inequality to establish the modified means. In the paper, we obtained the generalization of power mean, logarithms mean, arithmetic mean, Harmonic mean and geometric mean. The methodology adopted are Minkowski’s inequality and Hölder’s inequality to establish some means of order α of two distincts. These inequalities further generalize some existing results. This research work also demonstrated the importance of the Minkowski’s inequality and Hölder’s inequality over existing arithmetic mean, Harmonic mean and geometric mean and further extend the generalization to weighted logarithms mean. Hence, this article distinguished some present results on power mean, logarithms means and acquired more robust means by engaging modified Minkowski’s inequality and Hölder’s inequality with some ordinary theorems. The modified Minkowski’s inequality on power and logarithms mean further extends the generalized weighted logarithms mean of order α of two distincts. VL - 10 IS - 2 ER -