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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 904721, 7 pages
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.
- G. Pólya, “Ein mittelwertsatz für funktionen mehrerer veränderlichen,” Tohoku Mathematical Journal, vol. 19, pp. 1–3, 1921.
- G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, vol. 1, Springer, Berlin, Germany, 1925, German.
- G. Pólya and G. Szegö, Problems and Theorems in Analysis, vol. 1 of Classics in Mathematics, Springer, Berlin, Germany, 1972.
- G. Pólya and G. Szego, Problems and Theorems in Analysis, vol. 1, 1984, Chinese Edition.
- K. S. K. Iyengar, “Note on an inequality,” Math Students, vol. 6, pp. 75–76, 1938.
- 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.
- 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.
- F. Qi, “Inequalities for a multiple integral,” Acta Mathematica Hungarica, vol. 84, no. 1-2, pp. 19–26, 1999.
- F. Qi, “Inequalities for an integral,” The Mathematical Gazette, vol. 80, no. 488, pp. 376–377, 1996.
- 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.
- B.-N. Guo and F. Qi, “Estimates for an integral in norm of the -th derivative of its integrand,” in Inequality Theory and Applications, pp. 127–131, Nova Science Publishers, Hauppauge, NY, USA, 2003.
- B.-N. Guo and F. Qi, “Some estimates of an integral in terms of the -norm of the st derivative of its integrand,” Analysis Mathematica, vol. 29, no. 1, pp. 1–6, 2003.
- V. N. Huy and Q. A. Ngô, “On an Iyengar-type inequality involving quadratures in knots,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 289–294, 2010.
- F. Qi, “Further generalizations of inequalities for an integral,” Univerzitet u Beogradu Publikacije Elektrotehničkog Fakulteta, Serija: Matematika, vol. 8, pp. 79–83, 1997.
- F. Qi, “Inequalities for a weighted multiple integral,” Journal of Mathematical Analysis and Applications, vol. 253, no. 2, pp. 381–388, 2001.
- F. Qi and Y.-J. Zhang, “Inequalities for a weighted integral,” Advanced Studies in Contemporary Mathematics, vol. 4, no. 2, pp. 93–101, 2002.
- 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.
- 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.
- J. C. Kuang, Chángyòng Bùdĕng Shì (Applied Inequalities), Shandong Science and Technology Press Shandong Province, Jinan, China, 3rd edition, 2004, Chinese.
- 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.
- A. O. Akdemir, M. E. Özdemir, and S. Varošanec, “On some inequalities for -concave functions,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 746–753, 2012.
- 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.