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Some Integral Inequalities on Time Scales

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In the paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.

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References

  1. Agahi, H., Yaghoobi, M.A.: A Feng Qi type inequality for Sugeno integral. Fuzzy Inf. Eng. 2(3), 293–304 (2010). doi:10.1007/s12543-010-0051-8.

  2. Akkouchi M.: On an integral inequality of Feng Qi. Divulg. Mat. 13(1), 11–19 (2005)

    MathSciNet  MATH  Google Scholar 

  3. Akkouchi M.: Some integral inequalities. Divulg. Mat. 11(2), 121–125 (2003)

    MathSciNet  MATH  Google Scholar 

  4. Bohner M., Peterson A.: Dynamic equations on time scales: an introduction with applications. Birkhäuser, Boston (2001)

    Book  Google Scholar 

  5. Bougoffa, L.: An integral inequality similar to Qi’s inequality. J. Inequal. Pure Appl. Math. 6(1), Art. 27 (2005). http://www.emis.de/journals/JIPAM/article496.html

  6. Bougoffa, L.: Notes on Qi type integral inequalities. J. Inequal. Pure Appl. Math. 4(4), Art. 77 (2003). http://www.emis.de/journals/JIPAM/article318.html

  7. Brahim, K., Bettaibi, N., Sellemi, M.: On some Feng Qi type q-integral inequalities. J. Inequal. Pure Appl. Math. 9(2), Art. 43 (2008). http://www.emis.de/journals/JIPAM/article975.html

  8. Chai X.-K., Du H.-X.: Several discrete inequalities. Int. J. Math. Anal. 4(33–36), 1645–1649 (2010)

    MathSciNet  MATH  Google Scholar 

  9. Chen, Y., Kimball, J.: Note on an open problem of Feng Qi. J. Inequal. Pure Appl. Math. 7(1), Art. 4 (2006). http://www.emis.de/journals/JIPAM/article621.html

  10. Csiszár, V., Móri, T.F.: The convexity method of proving moment-type inequalities. Statist. Probab. Lett. 66(3), 303–313 (2004). doi:10.1016/j.spl.2003.11.007

  11. Dahmani Z., Tabharit L.: Certain inequalities involving fractional integrals. J. Adv. Res. Sci. Comput. 2(1), 55–60 (2010)

    MathSciNet  Google Scholar 

  12. Dahmani Z., Belarbi S.: Some inequalities of Qi type using fractional integration. Int. J Nonlinear Sci. 10(4), 396–400 (2010)

    MathSciNet  Google Scholar 

  13. Hong Y.: A note on Feng Qi type integral inequalities. Int. J. Math. Anal. (Ruse) 1(25–28), 1243–1247 (2007)

    MathSciNet  MATH  Google Scholar 

  14. Krasniqi V., Shabani A.Sh.: On some Feng Qi type h-integral inequalities. Int. J. Open Probl. Comput. Sci. Math. 2(4), 516–521 (2009)

    MathSciNet  MATH  Google Scholar 

  15. Liu, W.-J., Li, C.-C., Dong, J.-W.: Consolidations of extended Qi’s inequality and Bougoffa’s inequality. J. Math. Inequal. 2(1), 9–15 (2008). doi:10.7153/jmi-02-02

    Google Scholar 

  16. Liu, W.-J., Li, C.-C., Dong, J.-W.: Note on Qi’s inequality and Bougoffa’s inequality. J. Inequal. Pure Appl. Math. 7(4), Art. 129 (2006). http://www.emis.de/journals/JIPAM/article746.html

  17. Liu, W.-J., Ngô, Q.-A., Huy, V.N.: Several interesting integral inequalities. J. Math. Inequal. 3(2), 201–212 (2009). doi:10.7153/jmi-03-20

    Google Scholar 

  18. Mazouzi, S., Qi, F.: On an open problem regarding an integral inequality. J. Inequal. Pure Appl. Math. 4(2), Art. 31 (2003). http://www.emis.de/journals/JIPAM/article269.html

  19. Miao, Y.: Further development of Qi-type integral inequality. J. Inequal. Pure Appl. Math. 7(4), Art. 144 (2006). http://www.emis.de/journals/JIPAM/article763.html

  20. Miao, Y., Liu, J.-F.: Discrete results of Qi-type inequality. Bull. Korean Math. Soc. 46(1), 125-134 (2009). doi:10.4134/BKMS.2009.46.1.125

  21. Miao, Y., Qi, F.: Several q-integral inequalities. J. Math. Inequal. 3(1), 115–121 (2009). doi:10.7153/jmi-03-11

    Google Scholar 

  22. Ngô, Q.A., Tung, P.H.: Notes on an open problem of F. Qi and Y. Chen and J. Kimball. J. Inequal. Pure Appl. Math. 8(2), Art. 41 (2007). http://www.emis.de/journals/JIPAM/article856.html

  23. Pečarić, J., Pejković, T.: Note on Feng Qi’s integral inequality. J. Inequal. Pure Appl. Math. 5(3), Art. 51 (2004). http://www.emis.de/journals/JIPAM/article418.html

    Google Scholar 

  24. Pečarić, J., Pejković, T.: On an integral inequality. J. Inequal. Pure Appl. Math. 5(2), Art. 47 (2004). http://www.emis.de/journals/JIPAM/article401.html

    Google Scholar 

  25. Peters, G.W., Fan, Y., Sisson, S.A.: On sequential Monte Carlo, partial rejection control and approximate Bayesian computation. http://arxiv.org/abs/0808.3466v1

  26. Pogány, T.K.: On an open problem of F. Qi. J. Inequal. Pure Appl. Math. 3(4), Art. 54 (2002). http://www.emis.de/journals/JIPAM/article206.htm..

  27. Qi, F.: Several integral inequalities. J. Inequal. Pure Appl. Math. 1(2), Art. 19 (2000). http://www.emis.de/journals/JIPAM/article113.html

  28. Qi, F.: Several integral inequalities. RGMIA Res. Rep. Coll. 2(7), Art. 9, 1039–1042 (1999). http://rgmia.org/v2n7.php

  29. Qi, F., Li, A.-J., Zhao, W.-Z., Niu, D.-W., -Cao, J.: Extensions of several integral inequalities. J. Inequal. Pure Appl. Math. 7(3), Art. 107 (2006). http://www.emis.de/journals/JIPAM/article706.html

  30. Qi F., Yu K.-W.: Note on an integral inequality. J. Math. Anal. Approx. Theory 2(1), 96–98 (2007)

    MathSciNet  MATH  Google Scholar 

  31. Saitoh, S., Tuan, V.K., Yamamoto, M.: Reverse convolution inequalities and applications to inverse heat source problems. J. Inequal. Pure. Appl. Math. 3(5), Art. 80 (2002). http://www.emis.de/journals/JIPAM/article232.html

  32. Sarikaya, M.Z., Ozkan, U.M., Yildirim, H.: Time scale integral inequalities similar to Qi’s inequality. J. Inequal. Pure Appl. Math. 7(4), Art. 128 (2006). http://www.emis.de/journals/JIPAM/article745.html

  33. Sulaiman, W.T.: A study on new q-integral inequalities. Appl. Math. 2(4), 465–469 (2011). doi:10.4236/am.2011.24059

    Google Scholar 

  34. Sulaiman, W.T.: Several q-integral inequalities. Aust. J. Math. Anal. Appl. 7(2), Art. 6 (2010). http://ajmaa.org/cgi-bin/paper.pl?string=v7n2/V7I2P6.tex

  35. Sun, J.-S.: A note on an open problem for integral inequality. RGMIA Res. Rep. Coll. 7(3), Art. 21, 539–542 (2004). Available online at http://rgmia.org/v7n3.php

  36. Sun, J.-S., Wu Y.-Z.: Note on an open problem of inequality. College Math. (Dà àxué Shùxué) 24(1):126–128 (2008)

    Google Scholar 

  37. Towghi, N.: Notes on integral inequalities. RGMIA Res. Rep. Coll. 4(2), Art. 12, 277–278 (2001). http://rgmia.org/v4n2.php

  38. Witkowski, A.: On a F. Qi integral inequality. J. Inequal. Pure Appl. Math. 6(2), Art. 36 (2005). http://www.emis.de/journals/JIPAM/article505.html

  39. Yan, P., Gyllenberg, M.: On an open problem of integral inequalities. J. Inequal. Pure Appl. Math. 7(5), Art. 170 (2006). http://www.emis.de/journals/JIPAM/article788.html

    Google Scholar 

  40. Yan, P., Gyllenberg, M.: On a conjecture of Qi-type integral inequalities. J. Inequal. Pure. Appl. Math. 7(4), Art. 146 (2006). http://www.emis.de/journals/JIPAM/article760.html

  41. Yin L.: On several new Qi’s inequalities. Creat. Math. Inform. 20(1), 90–95 (2011)

    MathSciNet  MATH  Google Scholar 

  42. Yin, L., Luo, Q.-M., Qi, F.: Several integral inequalities on time scales. J. Math. Inequal. 6(3), 419–429 (2012). doi:10.7153/jmi-06-39

    Google Scholar 

  43. Yin, L., Qi, F.: Some integral inequalities on time scales. http://arxiv.org/abs/1105.1566

  44. Yu, K.-W., Qi, F.: A short note on an integral inequality. RGMIA Res. Rep. Coll. 4(1), Art. 4, 23–25 (2001). http://rgmia.org/v4n1.php

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Correspondence to Feng Qi.

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The first author was partially supported by the NSF of Shandong Province under grant numbers ZR2011AL001 and ZR2012AQ028.

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Yin, L., Qi, F. Some Integral Inequalities on Time Scales. Results. Math. 64, 371–381 (2013). https://doi.org/10.1007/s00025-013-0320-z

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  • DOI: https://doi.org/10.1007/s00025-013-0320-z

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