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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 901824, 9 pages
A New Reversed Version of a Generalized Sharp Hölder's Inequality and Its Applications
1College of Science and Technology, North China Electric Power University, Baoding 071000, China
2China Mobile Group Hebei Co., Ltd., Baoding 071000, China
Received 10 October 2012; Accepted 10 January 2013
Academic Editor: Pekka Koskela
Copyright © 2013 Jingfeng Tian and Xi-Mei Hu. 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.
- S. Abramovich, J. Pečarić, and S. Varošanec, “Sharpening Hölder's and Popoviciu's inequalities via functionals,” The Rocky Mountain Journal of Mathematics, vol. 34, no. 3, pp. 793–810, 2004.
- B. Ivanković, J. Pečarić, and S. Varošanec, “Properties of mappings related to the Minkowski inequality,” Mediterranean Journal of Mathematics, vol. 8, no. 4, pp. 543–551, 2011.
- B. Liu, “Inequalities and convergence concepts of fuzzy and rough variables,” Fuzzy Optimization and Decision Making, vol. 2, no. 2, pp. 87–100, 2003.
- L. Nikolova and S. Varošanec, “Refinements of Hölder's inequality derived from functions and ,” Annals of Functional Analysis, vol. 2, no. 1, pp. 72–83, 2011.
- S. M. Buckley and P. Koskela, “Ends of metric measure spaces and Sobolev inequalities,” Mathematische Zeitschrift, vol. 252, no. 2, pp. 275–285, 2006.
- I. Franjić, S. Khalid, and J. Pečarić, “Refinements of the lower bounds of the Jensen functional,” Abstract and Applied Analysis, vol. 2011, Article ID 924319, 13 pages, 2011.
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, 2nd edition, 1952.
- S. Hencl, P. Koskela, and X. Zhong, “Mappings of finite distortion: reverse inequalities for the Jacobian,” The Journal of Geometric Analysis, vol. 17, no. 2, pp. 253–273, 2007.
- K. Hu, “On an inequality and its applications,” Scientia Sinica, vol. 24, no. 8, pp. 1047–1055, 1981.
- R. Jiang and P. Koskela, “Isoperimetric inequality from the Poisson equation via curvature,” Communications on Pure and Applied Mathematics, vol. 65, no. 8, pp. 1145–1168, 2012.
- J. Kuang, Applied Inequalities, Shandong Science and Technology Press, Jinan, China, 4th edition, 2010.
- J. Mićić, Z. Pavić, and J. Pečarić, “Extension of Jensen's inequality for operators without operator convexity,” Abstract and Applied Analysis, vol. 2011, Article ID 358981, 14 pages, 2011.
- J. Tian, “Reversed version of a generalized sharp Hölder's inequality and its applications,” Information Sciences, vol. 201, pp. 61–69, 2012.
- J. Tian, “Inequalities and mathematical properties of uncertain variables,” Fuzzy Optimization and Decision Making, vol. 10, no. 4, pp. 357–368, 2011.
- J. Tian, “Extension of Hu Ke's inequality and its applications,” Journal of Inequalities and Applications, vol. 2011, article 77, 2011.
- J. Tian, “Property of a Hölder-type inequality and its application,” Mathematical Inequalities & Applications. In press.
- S. Varošanec, “A generalized Beckenbach-Dresher inequality and related results,” Banach Journal of Mathematical Analysis, vol. 4, no. 1, pp. 13–20, 2010.
- S. H. Wu, “Generalization of a sharp Hölder's inequality and its application,” Journal of Mathematical Analysis and Applications, vol. 332, no. 1, pp. 741–750, 2007.
- E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, Germany, 1983.
- J. Aczél, “Some general methods in the theory of functional equations in one variable. New applications of functional equations,” Uspekhi Matematicheskikh Nauk, vol. 11, no. 3, pp. 3–68, 1956 (Russian).
- T. Popoviciu, “On an inequality,” Gazeta Matematica şi Fizica A, vol. 11, pp. 451–461, 1959 (Romanian).
- J. Tian, “Reversed version of a generalized Aczél's inequality and its application,” Journal of Inequalities and Applications, vol. 2012, article 202, 2012.
- J. Tian and S. Wang, “Refinements of generalized Aczel’s inequality and Bellman’s inequality and their applications,” Journal of Applied Mathematics, vol. 2013, Article ID 645263, 6 pages, 2013.
- P. M. Vasić and J. E. Pečarić, “On the Hölder and some related inequalities,” Mathematica, vol. 25, no. 1, pp. 95–103, 1983.
- C.-L. Wang, “Characteristics of nonlinear positive functionals and their applications,” Journal of Mathematical Analysis and Applications, vol. 95, no. 2, pp. 564–574, 1983.
- M. Anwar, R. Bibi, M. Bohner, and J. Pečarić, “Integral inequalities on time scales via the theory of isotonic linear functionals,” Abstract and Applied Analysis, vol. 2011, Article ID 483595, 16 pages, 2011.
- X. He and Q.-M. Zhang, “Lyapunov-type inequalities for some quasilinear dynamic system involving the -Laplacian on time scales,” Journal of Applied Mathematics, vol. 2010, Article ID 418136, 10 pages, 2011.
- S. Hilger, “Analysis on measure chains—a unified approach to continuous and discrete calculus,” Results in Mathematics, vol. 18, no. 1-2, pp. 18–56, 1990.
- S. H. Saker, “Some new inequalities of Opial's type on time scales,” Abstract and Applied Analysis, vol. 2012, Article ID 683136, 14 pages, 2012.