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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 904721, 7 pages
http://dx.doi.org/10.1155/2013/904721
Research Article

Some Inequalities for Multiple Integrals on the -Dimensional Ellipsoid, Spherical Shell, and Ball

1College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Autonomous Region, Tongliao City 028043, China
2Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin City 300387, China
3School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China

Received 11 January 2013; Accepted 28 February 2013

Academic Editor: Josip E. Pečarić

Copyright © 2013 Yan Sun et al. 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. G. Pólya, “Ein mittelwertsatz für funktionen mehrerer veränderlichen,” Tohoku Mathematical Journal, vol. 19, pp. 1–3, 1921.
  2. G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, vol. 1, Springer, Berlin, Germany, 1925, German.
  3. G. Pólya and G. Szegö, Problems and Theorems in Analysis, vol. 1 of Classics in Mathematics, Springer, Berlin, Germany, 1972.
  4. G. Pólya and G. Szego, Problems and Theorems in Analysis, vol. 1, 1984, Chinese Edition.
  5. K. S. K. Iyengar, “Note on an inequality,” Math Students, vol. 6, pp. 75–76, 1938.
  6. R. P. Agarwal and S. S. Dragomir, “An application of Hayashi's inequality for differentiable functions,” Computers & Mathematics with Applications, vol. 32, no. 6, pp. 95–99, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. P. Cerone and S. S. Dragomir, “Lobatto type quadrature rules for functions with bounded derivative,” Mathematical Inequalities & Applications, vol. 3, no. 2, pp. 197–209, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Qi, “Inequalities for a multiple integral,” Acta Mathematica Hungarica, vol. 84, no. 1-2, pp. 19–26, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. F. Qi, “Inequalities for an integral,” The Mathematical Gazette, vol. 80, no. 488, pp. 376–377, 1996.
  10. B.-N. Guo and F. Qi, “Some bounds for the complete elliptic integrals of the first and second kinds,” Mathematical Inequalities & Applications, vol. 14, no. 2, pp. 323–334, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. B.-N. Guo and F. Qi, “Estimates for an integral in Lp norm of the (n+1)-th derivative of its integrand,” in Inequality Theory and Applications, pp. 127–131, Nova Science Publishers, Hauppauge, NY, USA, 2003. View at MathSciNet
  12. B.-N. Guo and F. Qi, “Some estimates of an integral in terms of the Lp-norm of the (n+1)st derivative of its integrand,” Analysis Mathematica, vol. 29, no. 1, pp. 1–6, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  13. V. N. Huy and Q. A. Ngô, “On an Iyengar-type inequality involving quadratures in n knots,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 289–294, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. F. Qi, “Further generalizations of inequalities for an integral,” Univerzitet u Beogradu Publikacije Elektrotehničkog Fakulteta, Serija: Matematika, vol. 8, pp. 79–83, 1997. View at Zentralblatt MATH · View at MathSciNet
  15. F. Qi, “Inequalities for a weighted multiple integral,” Journal of Mathematical Analysis and Applications, vol. 253, no. 2, pp. 381–388, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. F. Qi and Y.-J. Zhang, “Inequalities for a weighted integral,” Advanced Studies in Contemporary Mathematics, vol. 4, no. 2, pp. 93–101, 2002. View at Zentralblatt MATH · View at MathSciNet
  17. F. Qi, Z. L. Wei, and Q. Yang, “Generalizations and refinements of Hermite-Hadamard's inequality,” The Rocky Mountain Journal of Mathematics, vol. 35, no. 1, pp. 235–251, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Y. X. Shi and Z. Liu, “On Iyengar type integral inequalities,” Journal of Anshan University of Science and Technology, vol. 26, no. 1, pp. 57–60, 2003, Chinese.
  19. J. C. Kuang, Chángyòng Bùdĕng Shì (Applied Inequalities), Shandong Science and Technology Press Shandong Province, Jinan, China, 3rd edition, 2004, Chinese.
  20. F. Qi, “Polya type integral inequalities: origin, variants, proofs, refinements, generalizations, equivalences, and applications,” RGMIA Research Report Collection, 32 pages, 2013, http://rgmia.org/papers/v16/v16a20.pdf.
  21. A. O. Akdemir, M. E. Özdemir, and S. Varošanec, “On some inequalities for h-concave functions,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 746–753, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  22. C. P. Niculescu and L. E. Persson, Convex Functions and Their Applications, CMS Books in Mathematics, Springer, New York, NU, USA, 2006, A contemporary approach. View at MathSciNet