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Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It
Toyesh Prakash Sharma1
Section:Research Paper, Product Type: Journal-Paper
Vol.10 ,
Issue.2 , pp.33-37, Apr-2023
Online published on Apr 30, 2023
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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IEEE Style Citation: Toyesh Prakash Sharma, “Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.33-37, 2023.
MLA Style Citation: Toyesh Prakash Sharma "Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It." International Journal of Scientific Research in Mathematical and Statistical Sciences 10.2 (2023): 33-37.
APA Style Citation: Toyesh Prakash Sharma, (2023). Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It. International Journal of Scientific Research in Mathematical and Statistical Sciences, 10(2), 33-37.
BibTex Style Citation:
@article{Sharma_2023,
author = {Toyesh Prakash Sharma},
title = {Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {4 2023},
volume = {10},
Issue = {2},
month = {4},
year = {2023},
issn = {2347-2693},
pages = {33-37},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3104},
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3104
TI - Application of Jensen’s Inequality for Proving Nesbitt’s Inequality and Further Generalizing It
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Toyesh Prakash Sharma
PY - 2023
DA - 2023/04/30
PB - IJCSE, Indore, INDIA
SP - 33-37
IS - 2
VL - 10
SN - 2347-2693
ER -
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Abstract :
With the help of this article, the author is introducing new generalizations of a very popular inequality that we call Nesbitt’s inequality. For obtaining new generalizations, there is a use of another inequality called Jensen’s Inequality for convex functions, which is directly linked with derivatives of a function. There is a need for essential calculus and a better understanding of the proofs.
Key-Words / Index Term :
Jensen’s Inequality, Nesbitt’s Inequality Generalization, Convex function, Concave Function, Functional Inequalities, Three Variables etc.
References :
[1]. Nesbitt, A.M., Problem 15114, Educational Times, 55, 1902.
[2]. Jensen, J. L. W. V. "Sur les fonctions convexes et les inégalités entre les valeurs moyennes". Acta Mathematica. Vol. 30 issue 1: pp. 175–193, 1906.
[3]. Bakula, M.K., Nikodem, K.: Converse Jensen inequality for strongly convex set-valued maps. J. Math. Inequal. Vol. 12 issue 2, pp 545–550 2018.
[4]. Lu, G.: “New refinements of Jensen’s inequality and entropy upper bounds.” J. Math. Inequal. Vol. 12 issue 2, pp 403–421, 2018.
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