Year 2018,
Volume: 6 Issue: 1, 85 - 92, 27.04.2018
Tahir Ali
Muhammad Adil Khan
,
Adem Kilicman
,
Qamar Din
References
-
[1] Alomari, M. and Darus, M., The Hadamard’s inequality for s-convex functions of 2-variables on the co-ordinates,
Int. J. Math. Anal., 2(2008), 629-638.
-
[2] Alamori, M. and Darus, M., On the Hadamard’s inequality for log-convex functions on the coordinates, J.
Inequal. Appl., 2009, (2009): 283147.
-
[3] Chen, F., A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal.,
8, 4(2014), 915-923.
-
[4] Chu, Y. M., Khan, M. A., Ali, T. and Dragomir, S. S., Inequalities for α-fractional differentiable functions, J. Ineq.
Appl., 2017, (2017), 1-12.
-
[5] Chu, Y. M., Khan, M. A., Khan, T. U. and T. Ali, Generalizations of Hermite-Hadamard type inequalities for
MT-convex functions, J. Nonlinear Sci. Appl., 9, (2016), 4305–4316.
-
[6] Dragomir, S. S., Two Mappings in Connection to Hadamard’s Inequalities, J. Math. Anal, Appl., 167, (1992),
49–56.
-
[7] Dragomir, S. S., On the Hadamard’s inequality for convex function on the co-ordinates in a rectangle from the
plane, Taiwanese J. Math., 5, 4(2001), 775–788.
-
[8] Dragomir, S. S., Hermite-Hadamard’s type inequalities for operator convex functions, Appl. Math. Comput., 218,
3(2011), 766–772.
-
[9] Dragomir, S. S., Hermite-Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert
spaces, Linear Algebra Appl., 436, 5(2012), 1503-1515.
-
[10] Farissi, A. E., Simple proof and refinement of Hermite-Hadamard inequality, J. Math. Inequal., 4, 3(2010),
365–369.
-
[11] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier dune fonction considérée par `
Riemann, J. Math. Pures Appl., 58, (1893), 171-215.
-
[12] Gao, X., A note on the Hermite-Hadamard inequality, J. Math. Inequal., 4, 4(2010), 587–591.
-
[13] Bessenyei, M. and Páles, Z., Hadamard-type inequalities for generalized convex functions, Math. Inequal. Appl.,
6, 3(2003), 379–392.
-
[14] Iqbal, M., Bhatti, M. I. and Nazeer, K., Generalization of inequalities analogous to Hermite–Hadamard
inequality via fractional integrals, Bulletin of the Korean Math. Soc. 52(3) (2015), 707-716.
-
[15] Khan, M. A., Ali, T., Dragomir, S. S. and Sarikaya, M. Z., Hermite-Hadamard type inequalities for conformable
fractional integrals, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, 2017, 2017, 1–16.
-
[16] Latif, M. A. and Alomari, M., On Hadamard-type inequalities for h-convex functions on the coordinates, Int.
J.Math. Anal., 3, 33(2009), 1645–1656.
-
[17] Latif, M. A., and Dragomir, S. S., On some new inequalities for differentiable co-ordinated convex functions,J.
Inequal. Appl., 2012, (2012): 28.
-
[18] Nozdemir, M. E., Kavurmaci, H., Akdemir, A. O. and Avci, M., Inequalities for convex and s-convex functions
on ∆ = [a, b] × [c, d], J. Inequal. Appl., 2012, (2012): 20.
On the Refined Hermite-Hadamard Inequalities
Year 2018,
Volume: 6 Issue: 1, 85 - 92, 27.04.2018
Tahir Ali
Muhammad Adil Khan
,
Adem Kilicman
,
Qamar Din
Abstract
In this paper, we give some new refinements of Hermite-Hadamard inequality for co-ordinated convex
function. These refinements provide us better estimation as compare to the earlier established refinements
of Hadamard’s inequality.
References
-
[1] Alomari, M. and Darus, M., The Hadamard’s inequality for s-convex functions of 2-variables on the co-ordinates,
Int. J. Math. Anal., 2(2008), 629-638.
-
[2] Alamori, M. and Darus, M., On the Hadamard’s inequality for log-convex functions on the coordinates, J.
Inequal. Appl., 2009, (2009): 283147.
-
[3] Chen, F., A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal.,
8, 4(2014), 915-923.
-
[4] Chu, Y. M., Khan, M. A., Ali, T. and Dragomir, S. S., Inequalities for α-fractional differentiable functions, J. Ineq.
Appl., 2017, (2017), 1-12.
-
[5] Chu, Y. M., Khan, M. A., Khan, T. U. and T. Ali, Generalizations of Hermite-Hadamard type inequalities for
MT-convex functions, J. Nonlinear Sci. Appl., 9, (2016), 4305–4316.
-
[6] Dragomir, S. S., Two Mappings in Connection to Hadamard’s Inequalities, J. Math. Anal, Appl., 167, (1992),
49–56.
-
[7] Dragomir, S. S., On the Hadamard’s inequality for convex function on the co-ordinates in a rectangle from the
plane, Taiwanese J. Math., 5, 4(2001), 775–788.
-
[8] Dragomir, S. S., Hermite-Hadamard’s type inequalities for operator convex functions, Appl. Math. Comput., 218,
3(2011), 766–772.
-
[9] Dragomir, S. S., Hermite-Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert
spaces, Linear Algebra Appl., 436, 5(2012), 1503-1515.
-
[10] Farissi, A. E., Simple proof and refinement of Hermite-Hadamard inequality, J. Math. Inequal., 4, 3(2010),
365–369.
-
[11] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier dune fonction considérée par `
Riemann, J. Math. Pures Appl., 58, (1893), 171-215.
-
[12] Gao, X., A note on the Hermite-Hadamard inequality, J. Math. Inequal., 4, 4(2010), 587–591.
-
[13] Bessenyei, M. and Páles, Z., Hadamard-type inequalities for generalized convex functions, Math. Inequal. Appl.,
6, 3(2003), 379–392.
-
[14] Iqbal, M., Bhatti, M. I. and Nazeer, K., Generalization of inequalities analogous to Hermite–Hadamard
inequality via fractional integrals, Bulletin of the Korean Math. Soc. 52(3) (2015), 707-716.
-
[15] Khan, M. A., Ali, T., Dragomir, S. S. and Sarikaya, M. Z., Hermite-Hadamard type inequalities for conformable
fractional integrals, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, 2017, 2017, 1–16.
-
[16] Latif, M. A. and Alomari, M., On Hadamard-type inequalities for h-convex functions on the coordinates, Int.
J.Math. Anal., 3, 33(2009), 1645–1656.
-
[17] Latif, M. A., and Dragomir, S. S., On some new inequalities for differentiable co-ordinated convex functions,J.
Inequal. Appl., 2012, (2012): 28.
-
[18] Nozdemir, M. E., Kavurmaci, H., Akdemir, A. O. and Avci, M., Inequalities for convex and s-convex functions
on ∆ = [a, b] × [c, d], J. Inequal. Appl., 2012, (2012): 20.