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1. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
2. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
3. B. Liu, “Inequalities and convergence concepts of fuzzy and rough variables,” Fuzzy Optimization and Decision Making, vol. 2, no. 2, pp. 87–100, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
4. L. Nikolova and S. Varošanec, “Refinements of Hölder's inequality derived from functions ${\psi }_{p,q,\lambda }$ and ${\phi }_{p,q,\lambda }$,” Annals of Functional Analysis, vol. 2, no. 1, pp. 72–83, 2011. View at Zentralblatt MATH · View at MathSciNet
5. S. M. Buckley and P. Koskela, “Ends of metric measure spaces and Sobolev inequalities,” Mathematische Zeitschrift, vol. 252, no. 2, pp. 275–285, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
6. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
7. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, 2nd edition, 1952. View at MathSciNet
8. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
9. K. Hu, “On an inequality and its applications,” Scientia Sinica, vol. 24, no. 8, pp. 1047–1055, 1981. View at Zentralblatt MATH · View at MathSciNet
10. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
11. J. Kuang, Applied Inequalities, Shandong Science and Technology Press, Jinan, China, 4th edition, 2010.
12. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
13. J. Tian, “Reversed version of a generalized sharp Hölder's inequality and its applications,” Information Sciences, vol. 201, pp. 61–69, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
14. J. Tian, “Inequalities and mathematical properties of uncertain variables,” Fuzzy Optimization and Decision Making, vol. 10, no. 4, pp. 357–368, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
15. J. Tian, “Extension of Hu Ke's inequality and its applications,” Journal of Inequalities and Applications, vol. 2011, article 77, 2011.
16. J. Tian, “Property of a Hölder-type inequality and its application,” Mathematical Inequalities & Applications. In press.
17. S. Varošanec, “A generalized Beckenbach-Dresher inequality and related results,” Banach Journal of Mathematical Analysis, vol. 4, no. 1, pp. 13–20, 2010. View at Zentralblatt MATH · View at MathSciNet
18. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
19. E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, Germany, 1983. View at MathSciNet
20. 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). View at MathSciNet
21. T. Popoviciu, “On an inequality,” Gazeta Matematica şi Fizica A, vol. 11, pp. 451–461, 1959 (Romanian). View at Zentralblatt MATH · View at MathSciNet
22. J. Tian, “Reversed version of a generalized Aczél's inequality and its application,” Journal of Inequalities and Applications, vol. 2012, article 202, 2012.
23. 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. View at Publisher · View at Google Scholar
24. P. M. Vasić and J. E. Pečarić, “On the Hölder and some related inequalities,” Mathematica, vol. 25, no. 1, pp. 95–103, 1983. View at Zentralblatt MATH · View at MathSciNet
25. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
26. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
27. X. He and Q.-M. Zhang, “Lyapunov-type inequalities for some quasilinear dynamic system involving the $(p_1,p_2,\sum ,p_m)$-Laplacian on time scales,” Journal of Applied Mathematics, vol. 2010, Article ID 418136, 10 pages, 2011. View at MathSciNet
28. 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. View at Zentralblatt MATH · View at MathSciNet
29. 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. View at Zentralblatt MATH · View at MathSciNet