Hermite-Hadamard type inequalities for product of GA-convex functions via Hadamard fractional integrals
DOI:
https://doi.org/10.24193/subbmath.2017.4.04Keywords:
Hermite-Hadamard inequality, GA-convex functions, Hadamard fractional integral.Abstract
In this paper, some Hermite-Hadamard type inequalities for products of two GA-convex functions via Hadamard fractional integrals are established. Our results about GA-convex functions are analogous generalizations for some other results proved by Pachpette for convex functions.
Mathematics Subject Classification (2010): 26A51, 26A33, 26D10.
References
Bai, S.P., Wang, S.H., Qi, F., Some Hermite-Hadamard type inequalities for n-time differentiable (α, m)-convex functions, J. Inequal. Appl., 267(2012), 11 pages.
Bakula, M.K., O¨ zdemir, M.E., Peˇcari´c, J., Hadamard type inequalities form m-convex and (α, m)-convex functions, Journal of Inequalities in Pure and Applied Mathematics, 9(2008), no. 4, article 96.
Chen, F., On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity, Chinese Journal of Mathematics, Volume 2014, Article ID:173293, 2014.
Chen, F., A note on Hermite-Hadamard inequalities for products of convex functions, Journal of Applied Mathematics, Volume 2013, Article ID:935020, 2013.
Chen, F., A note on Hermite-Hadamard inequalities for products of convex functions via Riemann-Liouville fractional integrals, Italian Journal of Pure and Applied Mathematics, 33(2014), 299-306.
Chen, F., Wu, S., Some Hermite-Hadamard type inequalities for harmonically s-convex functions, The Scientific World Journal, Vol. 2014, Art. ID:279158, 2014.
Dragomir, S.S., Refinements of the Hermite-Hadamard integral inequality for log-convex functions, Aust. Math. Soc. Gaz., 28(2001), no. 3, 129-134.
Hadamard, J., E´tude sur les propri´et´es des fonctions enti`eres et en particulier d’une fonction consid´er´ee par Riemann, J. Math. Pures Appl., 58(1983), 171-215.
I˙¸scan, I˙., New general integral inequalities for quasi-geometrically convex functions via fractional integrals, J. Inequal. Appl., 491(2013), 15 pages.
I˙¸scan, I˙., Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43(2014), no. 6, 935-942.
Kırmacı, U.S., Bakula, M.K., O¨ zdemir, M.E., Peˇcari´c, J., Hadamard-type inequalities for s-convex functions, Applied Mathematics and Computation, 193(2007), no. 1, 26-35.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006.
Kunt, M., I˙¸scan, I˙., On new inequalities of Hermite-Hadamard-Fejer type for GA-convex functions via fractional integrals, RGMIA Research Report Collection, 18(2015), Art. 108, 12 pp.
Niculescu, C.P., Convexity according to the geometric mean, Math. Inequal. Appl., 3(2000), no. 2, 155-167.
Niculescu, C.P., Convexity according to means, Math. Inequal. Appl., 6(2003), no. 4, 571-579.
Pachpatte, B.G., On some inequalities for convex functions, RGMIA Research Report Collection E, vol. 6, 2003.
Pachpatte, B.G., A note on integral inequalities involving two log-convex functions, Mathematical Inequalities and Applications, 7(2004), no. 4, 511-515.
Rubinov, A.M., Dutta, J., Hadamard inequality for quasi-convex functions in higher dimensions, J. Math. Anal. Appl., 270(2002), 80-91.
Sarıkaya, M.Z., Sag˘lam, A., Yıldırım, H., On some Hadamard-type inequalities for h- convex functions, Journal of Mathematical Inequalities, 2(2008), no. 3, 335-341.
Yang, G.S., Refinements of Hadamard inequality for r-convex functions, Indian J. Pure Appl. Math., 32(2001), no. 10, 1571-1579.
Yin, H.P., Qi, F., Hermite-Hadamard type inequalities for the product of (α, m)-convex functions, Journal of Nonlinear Science and Applications, 8(2015), 231-236.
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