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Year 2018, Volume: 6 Issue: 1, 85 - 92, 27.04.2018

Tahir Ali Muhammad Adil Khan Adem Kilicman Qamar Din

https://doi.org/10.36753/mathenot.421769
Cited By: 3

Abstract

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

https://doi.org/10.36753/mathenot.421769
Cited By: 3

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.

Keywords

Convex function Co-ordinated convex function Hermite-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.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Tahir Ali This is me

Muhammad Adil Khan

Adem Kilicman

Qamar Din

Publication Date April 27, 2018
Submission Date March 17, 2016
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Ali, T., Khan, M. A., Kilicman, A., Din, Q. (2018). On the Refined Hermite-Hadamard Inequalities. Mathematical Sciences and Applications E-Notes, 6(1), 85-92. https://doi.org/10.36753/mathenot.421769
AMA Ali T, Khan MA, Kilicman A, Din Q. On the Refined Hermite-Hadamard Inequalities. Math. Sci. Appl. E-Notes. April 2018;6(1):85-92. doi:10.36753/mathenot.421769
Chicago Ali, Tahir, Muhammad Adil Khan, Adem Kilicman, and Qamar Din. “On the Refined Hermite-Hadamard Inequalities”. Mathematical Sciences and Applications E-Notes 6, no. 1 (April 2018): 85-92. https://doi.org/10.36753/mathenot.421769.
EndNote Ali T, Khan MA, Kilicman A, Din Q (April 1, 2018) On the Refined Hermite-Hadamard Inequalities. Mathematical Sciences and Applications E-Notes 6 1 85–92.
IEEE T. Ali, M. A. Khan, A. Kilicman, and Q. Din, “On the Refined Hermite-Hadamard Inequalities”, Math. Sci. Appl. E-Notes, vol. 6, no. 1, pp. 85–92, 2018, doi: 10.36753/mathenot.421769.
ISNAD Ali, Tahir et al. “On the Refined Hermite-Hadamard Inequalities”. Mathematical Sciences and Applications E-Notes 6/1 (April 2018), 85-92. https://doi.org/10.36753/mathenot.421769.
JAMA Ali T, Khan MA, Kilicman A, Din Q. On the Refined Hermite-Hadamard Inequalities. Math. Sci. Appl. E-Notes. 2018;6:85–92.
MLA Ali, Tahir et al. “On the Refined Hermite-Hadamard Inequalities”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 1, 2018, pp. 85-92, doi:10.36753/mathenot.421769.
Vancouver Ali T, Khan MA, Kilicman A, Din Q. On the Refined Hermite-Hadamard Inequalities. Math. Sci. Appl. E-Notes. 2018;6(1):85-92.

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