Research Article

Geometric interpretations and reversed versions of Young's integral inequality

Volume: 5 Number: 1 March 31, 2021
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. [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. [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. [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. [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. [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. [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. [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. [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

Authors

Aying Wan This is me
China

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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