Article on the applications of the Jensen’s Inequality in Alternative proofs and Problems

Toyesh Prakash Sharma¹

1. Department of Mathematics, Agra College, Agra, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.6 , pp.36-42, Dec-2022

Online published on Dec 31, 2022

Copyright © Toyesh Prakash Sharma . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Since as it is mentioned in the title that through this article there, we will deal with various applications of the classic Jensen’s Inequality more clearly Weighted Jensen’s Inequality of both kinds of a convex function and concave function. Under the title applications, we will mainly discuss two aspects of it which are the application of Jensen inequality in proving well-known inequalities such as AM-GM inequality, GM-HM inequality, Cauchy-Schwarz Inequality, Nesbitt’s inequality, weighted AM-GM inequality, Power Mean Inequality etc. and another aspect is the application of Jensen’s Inequality in solving and simplifying problems proposals published in different journals on the basis of it there are example problems for readers.

Key-Words / Index Term :
Jensen’s Inequality, Concave function, convex function, Weighted Jensen’s Inequality etc.

References :
[1] D. M. B ?atinet ?u-Giurgiu and Neculai Stanciu “Elementary Problem Solution Corner” B-1205, Fibonacci Quarterly Vol. 55 issue 1, p. 83 February 2017
[2] Goran Conar, Varaždin “Problem Solution Corner” Prob. 5673, School Science and Mathematics Journal, Vol. 122 issue-2, p.1, 2022.
[3] T. Andreescu, USA, and Marius St?nean “Problem Solution Corner” prob -O493, Mathematical Reflections, issue-5, p.3, 2019
[4] Toyesh Prakash Sharma “Problem Solution Corner” prob. U587. Mathematical Reflections, Issue-2, p.3, 2022
[5] J.L.D-Barrero “Elementary Problem Solution Corner” Prob. B-1255. Fibonacci Quarterly, Vol. 57, issue 3, p. 277, August 2019
[6] J.L.D-Barrero, Barcelona “Problem Solution Corner” Prob. 5096, School Science and Mathematics Journal, Vol. 110 Issue-4, p.12, 2010.
[7] T. Zvonaru “Problem Solution Corner” Prob. 5658, School Science and Mathematics Journal, Vol. 121 issue-11, p.2, 2021
[8] T. P. Sharma “Problem Solution Corner” Prob. U590. Mathematical Reflections, Issue-3 P.3, 2022
[9] Amengual, M. “Solution to Problem EM-55”. Arhimede math. j. Vol. 5 issue-2, pp. 159–160, 2018
[10] Daniel Sitaru “Problem Solution Corner” Prob. 5638, School Science and Mathematics Journal, Vol. 121 issue 11, p.6, 2021.
[11] G. Apostolopoulos “Problem Solution Corner” Prob. 4574, Crux Mathematicorum, Vol. 46 issue 8, p.415, October 2020
[12] G. Apostolopoulos “Problem Solution Corner” Prob. 4624, Crux Mathematicorum, Vol. 47 issue 3, p. 151, March 2021
[13] Toyesh Prakash Sharma, “Problem Solution Corner” Prob. 897, Pentagon, Vol. 81 issue 1 p.46, Fall 2021.
[14] Toyesh Prakash Sharma, “Problem Solution Corner” Prob. 907, Pentagon, Vol. 81 issue 2 p.67, Spring 2022.