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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 645263, 6 pages
http://dx.doi.org/10.1155/2013/645263
Research Article

Refinements of Generalized Aczél's Inequality and Bellman's Inequality and Their Applications

1College of Science and Technology, North China Electric Power University, Baoding, Hebei Province 071051, China
2Department of Mathematics and Computer, Baoding University, Baoding, Hebei Province 071000, China

Received 13 October 2012; Accepted 30 December 2012

Academic Editor: Shanhe Wu

Copyright © 2013 Jing-Feng Tian and Shu-Yan Wang. 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.

Linked References

  1. J. Aczél, “Some general methods in the theory of functional equations in one variable. New applications of functional equations,” Uspekhi Matematicheskikh Nauk, vol. 11, no. 3, pp. 3–68, 1956 (Russian). View at MathSciNet
  2. E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, Germany, 1983. View at MathSciNet
  3. J. L. Díaz-Barrero, M. Grau-Sánchez, and P. G. Popescu, “Refinements of Aczél, Popoviciu and Bellman's inequalities,” Computers & Mathematics with Applications, vol. 56, no. 9, pp. 2356–2359, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. Farid, J. Pečarić, and A. Ur Rehman, “On refinements of Aczél, Popoviciu, Bellman's inequalities and related results,” Journal of Inequalities and Applications, vol. 2010, Article ID 579567, 17 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, UK, 1952. View at MathSciNet
  6. D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Classical and New Inequalities in Analysis, vol. 61, Kluwer Academic, Dordrecht, The Netherlands, 1993. View at MathSciNet
  7. Y. Ouyang and R. Mesiar, “On the Chebyshev type inequality for seminormed fuzzy integral,” Applied Mathematics Letters, vol. 22, no. 12, pp. 1810–1815, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Popoviciu, “On an inequality,” Gazeta Matematica şi Fizica A, vol. 11, no. 64, pp. 451–461, 1959 (Romanian). View at Zentralblatt MATH · View at MathSciNet
  9. J. Tian, “Inequalities and mathematical properties of uncertain variables,” Fuzzy Optimization and Decision Making, vol. 10, no. 4, pp. 357–368, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. Tian, “Reversed version of a generalized Aczél's inequality and its application,” Journal of Inequalities and Applications, vol. 2012, article 202, 2012.
  11. J. Tian, “Reversed version of a generalized sharp Hölder's inequality and its applications,” Information Sciences, vol. 201, pp. 61–69, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Tian, “Extension of Hu Ke's inequality and its applications,” Journal of Inequalities and Applications, vol. 2011, article 77, 2011.
  13. J. Tian, “Property of a Hölder-type inequality and its application,” Mathematical Inequalities & Applications. In press.
  14. J. Tian and X. M. Hu, “A new reversed version of a generalized sharp Hölder's inequality and its applications,” Abstract and Applied Analysis. In press.
  15. P. M. Vasić and J. E. Pečarić, “On the Hölder and some related inequalities,” Mathematica, vol. 25, no. 1, pp. 95–103, 1982. View at Zentralblatt MATH · View at MathSciNet
  16. P. M. Vasić and J. E. Pečarić, “On the Jensen inequality for monotone functions,” Analele Universitatii din Timişoara, vol. 17, no. 1, pp. 95–104, 1979. View at Zentralblatt MATH · View at MathSciNet
  17. S. Vong, “On a generalization of Aczél's inequality,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1301–1307, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Wu and L. Debnath, “Generalizations of Aczél's inequality and Popoviciu's inequality,” Indian Journal of Pure and Applied Mathematics, vol. 36, no. 2, pp. 49–62, 2005. View at Zentralblatt MATH · View at MathSciNet
  19. W. Yang, “Refinements of generalized Aczél-Popoviciu's inequality and Bellman's inequality,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3570–3577, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. R. Bellman, “On an inequality concerning an indefinite form,” The American Mathematical Monthly, vol. 63, pp. 108–109, 1956. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet