EN
Geometric interpretations and reversed versions of Young's integral inequality
Abstract
The authors retrospect Young's integral inequality and its geometric interpretation, recall a reversed version of Young's integral inequality, present a geometric interpretation of the reversed version of Young's integral inequality, and conclude a new reversed version of Young's integral inequality.
The authors retrospect Young's integral inequality and its geometric interpretation, recall a reversed version of Young's integral inequality, present a geometric interpretation of the reversed version of Young's integral inequality, and conclude a new reversed version of Young's integral inequality. .
Keywords
References
- [1] D. R. Anderson, Young’s integral inequality on time scales revisited, J. Inequal. Pure Appl. Math. 8 (2007), no. 3, Art. 64; http://www.emis.de/journals/JIPAM/ article876.html.
- [2] R. P. Boas Jr. and M. B. Marcus, Generalizations of Young’s inequality, J. Math. Anal. Appl. 46 (1974), no. 1, 36–40; https://doi.org/10.1016/0022-247X(74)90279-0.
- [3] R. P. Boas Jr. and M. B. Marcus, Inequalities involving a function and its inverse, SIAM J.Math. Anal. 4 (1973), 585–591; https://doi.org/10.1137/0504051.
- [4] R. Cooper, Notes on certain inequalities: (1); Generalization of an inequality of W. H.Young, J. London Math. Soc. 2 (1927), no. 1, 17–21;https://doi.org/10.1112/jlms/s1-2.1.17.
- [5] R. Cooper, Notes on certain inequalities: II, J. London Math. Soc. 2 (1927), no. 3, 159–163; https://doi.org/10.1112/jlms/s1-2.3.159.
- [6] F. Cunningham, Jr. and N. Grossman, On Young’s inequality, Amer. Math. Monthly 78 (1971), no. 7, 781–783; https://doi.org/10.2307/2318018.
- [7] J. B. Diaz and F. T. Metcalf, An analytic proof of Young’s inequality, Amer. Math. Monthly 77 (1970), no. 6, 603–609;https://doi.org/10.2307/2316736.
- [8] A. Hoorfar and F. Qi, A new refinement of Young’s inequality, Math. Inequal. Appl. 11 (2008), no. 4, 689–692; https://doi.org/10.7153/mia-11-58.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
March 31, 2021
Submission Date
October 27, 2020
Acceptance Date
December 25, 2020
Published in Issue
Year 2021 Volume: 5 Number: 1
APA
Qi, F., & Wan, A. (2021). Geometric interpretations and reversed versions of Young’s integral inequality. Advances in the Theory of Nonlinear Analysis and Its Application, 5(1), 1-6. https://doi.org/10.31197/atnaa.817804
AMA
1.Qi F, Wan A. Geometric interpretations and reversed versions of Young’s integral inequality. ATNAA. 2021;5(1):1-6. doi:10.31197/atnaa.817804
Chicago
Qi, Feng, and Aying Wan. 2021. “Geometric Interpretations and Reversed Versions of Young’s Integral Inequality”. Advances in the Theory of Nonlinear Analysis and Its Application 5 (1): 1-6. https://doi.org/10.31197/atnaa.817804.
EndNote
Qi F, Wan A (March 1, 2021) Geometric interpretations and reversed versions of Young’s integral inequality. Advances in the Theory of Nonlinear Analysis and its Application 5 1 1–6.
IEEE
[1]F. Qi and A. Wan, “Geometric interpretations and reversed versions of Young’s integral inequality”, ATNAA, vol. 5, no. 1, pp. 1–6, Mar. 2021, doi: 10.31197/atnaa.817804.
ISNAD
Qi, Feng - Wan, Aying. “Geometric Interpretations and Reversed Versions of Young’s Integral Inequality”. Advances in the Theory of Nonlinear Analysis and its Application 5/1 (March 1, 2021): 1-6. https://doi.org/10.31197/atnaa.817804.
JAMA
1.Qi F, Wan A. Geometric interpretations and reversed versions of Young’s integral inequality. ATNAA. 2021;5:1–6.
MLA
Qi, Feng, and Aying Wan. “Geometric Interpretations and Reversed Versions of Young’s Integral Inequality”. Advances in the Theory of Nonlinear Analysis and Its Application, vol. 5, no. 1, Mar. 2021, pp. 1-6, doi:10.31197/atnaa.817804.
Vancouver
1.Feng Qi, Aying Wan. Geometric interpretations and reversed versions of Young’s integral inequality. ATNAA. 2021 Mar. 1;5(1):1-6. doi:10.31197/atnaa.817804
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Advances in the Theory of Nonlinear Analysis and its Application
https://doi.org/10.31197/atnaa.1003964