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http://dx.doi.org/10.14317/jami.2015.119

REFINEMENTS OF HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS  

Xiang, Ruiyin (School of Mathematics and Statistics, Chongqing Three-Gorges University)
Publication Information
Journal of applied mathematics & informatics / v.33, no.1_2, 2015 , pp. 119-125 More about this Journal
Abstract
In this note, two new mappings associated with convexity are propoesd, by which we obtain some new Hermite-Hadamard type inequalities for convex functions via Riemann-Liouville fractional integrals. We conclude that the results obtained in this work are the refinements of the earlier results.
Keywords
Hermite-Hadamard inequality; convex function; Riemann-Liouville fractional integrals;
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1 S. Abramovich, G. Farid, and J. Pecaric, More about Hermite-Hadamard inequalities, Cauchy's means, and superquadracity, J. Inequal. Appl., 2010 (2010), Article ID 102467.
2 M. Bessenyei and Z. Pales, Hadamard-type inequalities for generalized convex functions, Math. Inequal. Appl., 6 (2003), 379-392.
3 F.X. Chen, On Hermite-Hadamard type inequalities for s-convex functions on the coordinates via Riemann-Liouville fractional integrals, J. Appl. Math., 2014 (2014), Article ID 248710, 8 pages.
4 S.S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.   DOI
5 S.S. Dragomir and G.H. Toader, Some inequalities for m-convex functions, Stud. Univ. Babes-Bolyai Math., 38 (1993), 21-28.
6 S.S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math., 32 (1999), 687-696.
7 A.E. Farissi, Simple proof and refinement of Hermite-Hadamard inequality, J. Math. Inequal., 4 (2010), 365-369.
8 X. Gao, A note on the Hermite-Hadamard inequality, J. Math. Inequal., 4 (2010), 587-591.
9 U.S. Kirmaci, M.K. Bakula, M.E. Ozdemir, J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 1 (2007), 26-35.
10 M.Z. Sarikaya et al, On some Hadamard-type inequalities for h-convex functions, J. Math. Inequal., 2 (2008), 335-341.
11 M.Z. Sarikaya et al, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (2013), 2403-2407.   DOI   ScienceOn
12 G.S. Yang and K.L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.   DOI   ScienceOn
13 G.S. Yang and M.C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37.