Hermite-Hadamard type inequalities for product of GA-convex functions via Hadamard fractional integrals

Imdat Iscan, Mehmet Kunt


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.


Hermite-Hadamard inequality, GA-convex functions, Hadamard fractional integral.

Full Text:



M. K. Bakula, M. E. Özdemir, and J. Peµcari´ c, Hadamard type inequalities form m-convex

and (;m)-convex functions, Journal of Inequalities in Pure and Applied Mathematics, vol.

, no. 4, article 96, 2008.

S-P Bai, S-H Wang and F. Qi , Some HermiteHadamard type inequalities for n-time di¤er-

entiable (;m)-convex functions, J. Inequal. Appl. (2012) 267, 2012, 11 pages.

F. Chen, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals

via two kinds of convexity, Chinese Journal of Mathematics, Volume 2014, Article ID:173293,

F. Chen, A note on Hermite-Hadamard inequalities for Products of convex functions, Journal

of Applied Mathematics, Volume 2013, Article ID:935020, 2013.

F. Chen, A note on Hermite-Hadamard inequalities for products of convex functions via

Riemann-Liouville fractional integrals, Italian Journal of Pure and Applied Mathematics, N.

(299-306), 2014.

F. Chen, S. Wu, Some Hermite-Hadamard type inequalities for harmonically s-convex func-

tions, The Scienti c World Journal, Volume 2014, Article ID:279158, 2014.

S. S. Dragomir, Re nements of the Hermite-Hadamard integral inequality for log-convex

functions . Aust. Math. Soc. Gaz. 28(3), 129134, 2001.

J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier dune fonction

considérée par Riemann, J. Math. Pures Appl., 58, 171-215, 1893.

·I. ·I¸scan, New general integral inequalities for quasi-geometrically convex functions via frac-

tional integrals, J. Inequal. Appl., 2013(491) (2013), 15 pages.

·I. ·I¸scan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J.

Math. Stat., 43 (6), 935-942, 2014.

U. S. K¬rmac¬, M. K. Bakula, M. E. Özdemir, and J. Peµcari´ c, Hadamard-type inequalities

for s-convex functions, Applied Mathematics and Computation, vol. 193, no. 1, pp. 2635,

M. Kunt, ·I. ·I¸scan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex func-

tions via fractional integrals, RGMIA Research Report Collection, 18(2015), Article 108, 12


A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional di¤erential

equations. Elsevier, Amsterdam (2006).

C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2),

-167, 2000. Available online at http://dx.doi.org/10.7153/mia-03-19.

C. P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (4), 571-579, 2003.

Available online at http://dx.doi.org/10.7153/mia-06-53.

B. G. Pachpatte, On some inequalities for convex functions, RGMIA Research Report Col-

lection E, vol. 6, 2003.

B. G. Pachpatte, A note on integral inequalities involving two log-convex functions, Mathe-

matical Inequalities and Applications, vol. 7, no. 4, pp. 511515, 2004.

A.M. Rubinov, J. Dutta, Hadamard inequality for quasi-convex functions in higher dimen-

sions, J. Math. Anal. Appl., 270, pp. 8091, 2002.

M. Z. Sar¬kaya, A. Sa¼glam, and H. Y¬ld¬r¬m, On some Hadamard-type inequalities for h-

convex functions, Journal of Mathematical Inequalities, vol. 2, no. 3, pp. 335341, 2008.

G. S. Yang, Re nements of Hadamard inequality for r-convex functions . Indian J. Pure Appl.

Math.. 32(10), 15711579, 2001.

H.-P. Yin, F. Qi, Hermite-Hadamard type inequalities for the product of (;m)-convex func-

tions, Journal of Nonlinear Science and Applications, 8 (231-236), 2015.

DOI: http://dx.doi.org/10.24193/subbmath.2017.4.04


  • There are currently no refbacks.