Some New Inequalities of Qi Type for Definite Integrals

Main Article Content

Bo-Yan Xi, Feng Qi

Abstract

In the paper, the authors establish some new integral inequalities, from which some integral inequalities of Qi type may be derived.

Article Details

References

  1. M. Akkouchi, On an integral inequality of Feng Qi, Divulg. Mat. 13 (2005), no. 1, 11-19.
  2. K. Brahim, N. Bettaibi, and M. Sellemi, On some Feng Qi type q-integral inequalities, J. Inequal. Pure Appl. Math. 9 (2008), no. 2, Art. 43; Available online at http://www.emis.de/journals/JIPAM/article975.html.
  3. Y. Chen and J. Kimball, Note on an open problem of Feng Qi, J. Inequal. Pure Appl. Math. 7 (2006), no. 1, Art. 4; Available online at http://www.emis.de/journals/JIPAM/article621.html.
  4. V. Csisz ´ar and T. F. M ´ori, The convexity method of proving moment-type inequalities, Statist. Probab. Lett. 66 (2004), no. 3, 303-313; Available online at http://dx.doi.org/10.1016/j.spl.2003.11.007.
  5. J.-C. Kuang, Applied Inequalities, 3rd edition, Shandong Science and Technology Press, Ji'nan City, China, 2004. (Chinese)
  6. S. Mazouzi and F. Qi, On an open problem regarding an integral inequality, J. Inequal. Pure Appl. Math. 4 (2003), no. 2, Art. 31; Available online at http://www.emis.de/journals/JIPAM/article269.html.
  7. Y. Miao, Further development of Qi-type integral inequality, J. Inequal. Pure Appl. Math. 7 (2006), no. 4, Art. 144; Available online at http://www.emis.de/journals/JIPAM/article763.html.
  8. Y. Miao and J.-F. Liu, Discrete results of Qi-type inequality, Bull. Korean Math. Soc. 46 (2009), no. 1, 125-134; Available online at http://dx.doi.org/10.4134/BKMS.2009.46.1.125.
  9. Y. Miao and F. Qi, Several q-integral inequalities, J. Math. Inequal. 3 (2009), no. 1, 115-121; Available online at http://dx.doi.org/10.7153/jmi-03-11.
  10. T. K. Pog ´any, On an open problem of F. Qi, J. Inequal. Pure Appl. Math. 3 (2002), no. 4, Art. 54; Available online at http://www.emis.de/journals/JIPAM/article206.html.
  11. F. Qi, Several integral inequalities, J. Inequal. Pure Appl. Math. 1 (2000), no. 2, Art. 19; Available online at http://www.emis.de/journals/JIPAM/article113.html.
  12. F. Qi, Several integral inequalities, RGMIA Res. Rep. Coll. 2 (1999), no. 7, Art. 9, 1039-1042; Available online at http://rgmia.org/v2n7.php.
  13. F. Qi, A.-J. Li, W.-Z. Zhao, D.-W. Niu, and J.-Cao, Extensions of several integral inequalities, J. Inequal. Pure Appl. Math. 7 (2006), no. 3, Art. 107; Available online at http://www.emis.de/journals/JIPAM/article706.html.
  14. F. Qi and K.-W. Yu, Note on an integral inequality, J. Math. Anal. Approx. Theory 2 (2007), no. 1, 96-98.
  15. N. Towghi, Notes on integral inequalities, RGMIA Res. Rep. Coll. 4 (2001), no. 2, Art. 12, 277-278; Available online at http://rgmia.org/v4n2.php.
  16. S.-H. Wu, rP -convex function and Jensen's type inequality, Math. Pract. Theory 35 (2005), no. 3, 220-228. (Chinese)
  17. B.-Y. Xi and T.-Y. Bao, On some properties of r-mean convex function, Math. Pract. Theory 38 (2008), no. 12, 113-119. (Chinese)
  18. B.-Y. Xi and F. Qi, Some inequalities of Qi type for double integrals, J. Egyptian Math. Soc. (2014), in press; Available online at http://dx.doi.org/10.1016/j.joems.2013.11.002.
  19. L. Yin, Q.-M. Luo, and F. Qi, Several integral inequalities on time scales, J. Math. Inequal. 6 (2012), no. 3, 419-429; Available online at http://dx.doi.org/10.7153/jmi-06-39.
  20. L. Yin and F. Qi, Some integral inequalities on time scales, Results Math. 64 (2013), no. 3, 371-381; Available online at http://dx.doi.org/10.1007/s00025-013-0320-z.