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107.32 A new inductive proof of the AM - GM inequality

Published online by Cambridge University Press:  11 October 2023

Romeo Meštrović
Romeo Meštrović*
Affiliation:
Maritime Faculty Kotor, University of Montenegro Dobrota 36, 85 330 Kotor, Montenegro e-mail: romeo@ucg.ac.me
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Abstract

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Information
The Mathematical Gazette , Volume 107 , Issue 570 , November 2023 , pp. 497 - 499
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Copyright
© The Authors, 2023 Published by Cambridge University Press on behalf of The Mathematical Association

References

Mitrinović, D. S., Handbook of means and their inequalities, Springer (1971).Google Scholar
Cvetkovski, Z., Inequalities (theorems, techniques and selected problems), Springer (2012).CrossRefGoogle Scholar
Bullen, P. S., Handbook of Means and their inequalities, Dordrecht: Kluwer Academic Publishers (2003).CrossRefGoogle Scholar
Chong, K. M., An inductive proof of the A.M. - G.M. inequality, Amer. Math. Monthly 83(2) (1976) pp. 87–88.CrossRefGoogle Scholar
Genčev, M., On a proof of the inequality between the arithmetic and geometric means, Amer. Math. Monthly 125(7) (2018) pp. 650–652.CrossRefGoogle Scholar
Rüthing, D., Proofs of the arithmetic-geometric mean inequality, Int. J. Math. Educ. Sci. Technol. 13(1) (1982) pp. 49–54.CrossRefGoogle Scholar
Uchida, Y., A simple proof of the geometric-arithmetic mean inequality, J. Inequ. Pure Appl. Math. 9(2) (2008), Article 56.Google Scholar
Urmanian, Z., An inductive proof of the geometric-arithmetic mean inequality, Math. Gaz. 84(499) (March 2008), pp. 101–102.CrossRefGoogle Scholar
Cauchy, A. L., Cours d’analyse de l'École Royale Polytechnique, première partie, Analyse algébrique, Paris (1821).Google Scholar
Beckenbach, E. F. and Bellman, R., Inequalities (3rd edn.), Ergebnisse der Mathematik, Band 30, Springer-Verlag, Berlin and New York (1971). Google Scholar