Some New Inequalities of Qi Type for Definite Integrals

Xi, Bo-Yan; Qi, Feng

Research Article

Some New Inequalities of Qi Type for Definite Integrals

Bo-Yan Xi
Feng Qi*

* Corresponding author

Abstract

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

How to Cite

B.-Y. Xi, F. Qi, Some New Inequalities of Qi Type for Definite Integrals, Int. J. Anal. Appl. 5 (2014), 20–26.

BibTeX

@article{Xi2014,
  author  = {Xi, Bo-Yan and Qi, Feng},
  title   = {Some New Inequalities of Qi Type for Definite Integrals},
  journal = {Int. J. Anal. Appl.},
  volume  = {5},
  year    = {2014},
  pages   = {20--26},
  doi     = {}
}

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.