THERMAL SCIENCE

International Scientific Journal

Wen-Ting Luo

,

You-Jun Zhou

,

Hai-Miao Meng

,

Lu-Wei Tang

SOME INTEGRAL INEQUALITIES ON PROBABILITY SPACE

ABSTRACT
Holder’s inequality and Minkowski’s inequality are important tools in probability theory and mathematical analysis and they have wide applications in many branches of mathematics. This paper studies the reverse probability inequalities of these, as well as their generalizations and improvements.
KEYWORDS
Holder’s inequality, Minkowski’s inequality, Young inequality, reverse probability inequality
PAPER SUBMITTED: 2024-07-01
PAPER REVISED: 2024-10-01
PAPER ACCEPTED: 2024-11-21
PUBLISHED ONLINE: 2025-05-03
DOI REFERENCE: https://doi.org/10.2298/TSCI2502083L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 2, PAGES [1083 - 1088]
REFERENCES
  1. Hamzeh, A., et al., Probability Inequalities for Decomposition Integrals, Journal of Computational and Applied Mathematics, 315 (2017), May, pp. 240-248
  2. Beckenbach, E. F., et al., Inequalities, Springer-Verlag, Berlin, Germany, 1961
  3. Hardy, G. H., et al., Inequalities, Cambridge University Press, Cambridge, UK, 1952
  4. Barnes, D. C., Supplements of Holder's Inequality, Canadian Journal of Mathematics, 36 (1984), 3, pp. 405-420
  5. Cheung, W. S., et al., Generalizations of Holder's Inequality, International Journal of Mathematics and Mathematical Sciences, 26 (2001), 1, pp. 7-10
  6. Didenko, V. D., et al., Power Means and the Reverse Holder Inequality, Studia Mathematica, 207 (2011), 1, pp. 85-95
  7. Berndt, R., The Weighted Fourier Inequality, Polarity, and Reverse Hölder Inequality, Journal of Fourier Analysis and Applications, 24 (2018), 4, pp. 1518-1538
  8. Chen, G. S., et al., The Diamond Integral Reverse Holder Inequality and Related Results on Time, Advances in Difference Equations, 2015 (2015), 3, pp. 1-20
  9. Bourin, J. C.,et al., Jensen and Minkowski Inequalities for Operator Means and Anti-Norms, Linear Algebra and its Applications, 456 (2014), 3, pp. 22-53
  10. Matkowski, J., The Pexider Type Generalization of the Minkowski Inequality, Journal of Mathematical Analysis and Applications, 393 (2012), 1, pp. 298-310
  11. Agahi, H., et al., H0lder and Minkowski Type Inequalities for Pseudo-Integral, Applied Mathematics and Computation, 217 (2011), 21, pp. 8630-8639
  12. Xing, J., et al., The Applications of Young Inequality and Young Inverse Inequality, Journal of Zhoukou Normal University, 24 (2007), 2, pp. 37-39
  13. El-Deeb, A. A., et al., Some Reverse Hölder Inequalities with Specht's Ratio on Time Scales, Journal of Non-Linear Sciences and Applications, 11 (2018), 3, pp. 444-455
  14. Zhao, C. J., et al., Hölder's Reverse Inequality and Its Applications, Publications de l'Institut Mathematique, 99 (2016), 2, pp. 211-216
  15. Wu, L., et al., Holder Type Inequality for Sugeno Integral, Fuzzy Sets and Systems, 161 (2010), 1, pp. 2337-2347
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Some integral inequalities on probability space

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence