Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 6 Sayı: 1, 85 - 92, 27.04.2018
https://doi.org/10.36753/mathenot.421769

Öz

Kaynakça

  • [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

Yıl 2018, Cilt: 6 Sayı: 1, 85 - 92, 27.04.2018
https://doi.org/10.36753/mathenot.421769

Öz

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.

Kaynakça

  • [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.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Tahir Ali Bu kişi benim

Muhammad Adil Khan

Adem Kilicman

Qamar Din

Yayımlanma Tarihi 27 Nisan 2018
Gönderilme Tarihi 17 Mart 2016
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

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. Nisan 2018;6(1):85-92. doi:10.36753/mathenot.421769
Chicago Ali, Tahir, Muhammad Adil Khan, Adem Kilicman, ve Qamar Din. “On the Refined Hermite-Hadamard Inequalities”. Mathematical Sciences and Applications E-Notes 6, sy. 1 (Nisan 2018): 85-92. https://doi.org/10.36753/mathenot.421769.
EndNote Ali T, Khan MA, Kilicman A, Din Q (01 Nisan 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, ve Q. Din, “On the Refined Hermite-Hadamard Inequalities”, Math. Sci. Appl. E-Notes, c. 6, sy. 1, ss. 85–92, 2018, doi: 10.36753/mathenot.421769.
ISNAD Ali, Tahir vd. “On the Refined Hermite-Hadamard Inequalities”. Mathematical Sciences and Applications E-Notes 6/1 (Nisan 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 vd. “On the Refined Hermite-Hadamard Inequalities”. Mathematical Sciences and Applications E-Notes, c. 6, sy. 1, 2018, ss. 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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