Some Hermite-Hadamard type inequalities obtain via Riemann-Liouville fractional calculus
Keywords:convex function, Hermite-Hadamard inequality, Riemann-Liouville fractional integrals.
AbstractWe provide some new Hermite-Hadamard type inequalities for functions whose derivatives in absolute value are convex, via Riemann-Liouville fractional integration.
S. S. Dragomir, C. E. M. Pearce, Selected Topic on Hermite-Hadamard Inequalities and Applications, Melbourne and Adelaide, December, 2000.
R. Gorenflo, F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, Springer Verlag, Wien, 1997.
H. Kavurmaci, M. Avci, M. E. Ozdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, arXiv: 1006.1593v1[math. CA].
M. A. Latif, New inequalities of Hermite-Hadamard type For functions whose derivatives in absolute value are convex with applications, RGMIA Research Report Collection, 15 (2012), Article 34, 13 pp.
C. P. Niculescu, L.-E. Persson, Convex Functions and their Applications. A Contemporary Approach. CMS Books in Mathematics vol. 23, Springer-Verlag, New York, 2006.