SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 70 Issue: 1

Hermite-Hadamard-Fejér inequalities for double integrals

Hüseyin Budak(DUZCE UNIVERSITY)0000-0001-8843-955X
Mehmet Zeki Sarıkaya(DUZCE UNIVERSITY)0000-0002-6165-9242
Pages
—
Publication Date
2021-06-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The inequalities obtained in this study provide generalizations of some result given in earlier works.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we first obtain Hermite-Hadamard-Fejer inequalities for co-ordinated convex functions in a rectangle from the plane R 2 .
📊
Key Findings & Data:Moreover, we give the some refinement of these obtained Hermite-Hadamard-Fejer inequalities utilizing two mapping.
💡
Conclusion & Impact:The inequalities obtained in this study provide generalizations of some result given in earlier works.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hermite-Hadamard-Fejer inequalities · co-ordinated convex · integral inequalities

Abstract

In this paper, we first obtain Hermite-Hadamard-Fejer inequalities for co-ordinated convex functions in a rectangle from the plane R 2 . Moreover, we give the some refinement of these obtained Hermite-Hadamard-Fejer inequalities utilizing two mapping. The inequalities obtained in this study provide generalizations of some result given in earlier works.

🔖

Cite This Article

Budak, H., Sarıkaya, M. Z. (2021). Hermite-Hadamard-Fejér inequalities for double integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 70 Issue: 1. https://doi.org/10.31801/cfsuasmas.748013

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (32)

  1. M. Alomari and M. Darus: The Hadamards inequality for s-convex function of 2-variables on the coordinates. Int. J. Math. Anal. 2(13), 629-638 (2008).
  2. M. Alomari and M. Darus, Fejér inequality for double integrals, Facta Universitatis (NIS), Ser. Math. Inform. 24 (2009), 15-28.
  3. T. Ali, M. A. Khan, A. Kilicman and Q. Din, On the refined Hermite-Hadamard inequalities, Mathematical Sciences & Applications E-Notes, 6 (1) 85-92 (2018).
  4. A.G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28 (1994), 7-12.
  5. M. K. Bakula, An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates, Australian Journal of Mathematical Analysis and Applications, 11(1) (2014), 1-7.
  6. F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal., 8(4), (2014), 915-923.
  7. S.S. Dragomir, On Hadamards inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwan. J. Math. 4, 775–788 (2001).
  8. S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  9. S.S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones J. Math. 37(4), 343–341 (2015).
  10. S.S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.
  11. S.S. Dragomir, J.Pecaric, L.E. Persson, Some inequalities of Hadamard type. Soochow J. Math. 21, 335-341 (1995).
  12. G. Farid, M. Marwan and Atiq Ur Rehman, Fejer-Hadamard inequlality for convex functions on the co-ordinates in a rectangle from the plane, International Journal of Analysis and Applications 10(1), (2016), 40-47.
  13. L. Fejer, Über die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369-390. (Hungarian).
  14. U.S. Kırmacı, M.K. Bakula, M.E. Özdemir, J. Peµcari´c, Hadamard-tpye inequalities for s-convex functions, Appl. Math. Comput. 193 (2007) 26-35.
  15. M. A. latif, S. Hussain and S. S. Dragomir, On some new Fejer-type inequalities for coordinated convex functions, TJMM, 3 (2011), No. 2, 57-80.
  16. M. A. latif, On some Fejer-type inequalities for double integrals, Tamkang Journal of Mathematics, 43(3), 2012, 423-436.
  17. M. A. Latif, S. S. Dragomir, and E. Momoniat, Weighted generalization of some integral inequalities for differentiable co-ordinated convex functions, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 78 (2016), no. 4, 197-210.
  18. M. A. Latif, S. S. Dragomir, and E. Momoniat, Generalization of some Inequalities for differentiable co-ordinated convex functions with applications, Moroccan J. Pure and Appl. Anal. 2(1), 2016, 12-32.
  19. M. A. Latif and S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 2012, (2012): 28.
  20. M.E. Ozdemir, C. Yildiz and A.O. Akdemir, On the co-ordinated convex functions Appl. Math. Inf. Sci. 8(3), 1085-1091 (2014). Z. Pavic, Improvements of the Hermite-Hadamard inequality, Journal of Inequalities and Applications (2015) 2015:222
  21. J. E. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  22. M. Z. Sarikaya, E. Set, M. E. Ozdemir and S. S. Dragomir, New some Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2) (2012) 137-152.
  23. E. Set, M.E. Özdemir, S.S. Dragomir, On the Hermite-Hadamard inequality and other integral inequalities involving two functions, J. Inequal. Appl. (2010) 9. Article ID 148102.
  24. K. L. Tseng and S. R. Hwang, New Hermite-Hadamard inequalities and their applications, Filomat, 30(14), 2016, 3667-3680.
  25. D. Y. Wang, K.L. Tseng and G. S. Yang, Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane. Taiwan. J. Math. 11, 63-73 (2007).
  26. B.Y. Xi, J. Hua and F. Qi, Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle. J. Appl. Anal. 20(1), 1–17 (2014).
  27. R. Xiang and F. Chen, On some integral inequalities related to Hermite-Hadamard-Fejér inequalities for coordinated convex functions, Chinese Journal of Mathematics, Volume 2014, Article ID 796132, 10 pages
  28. G. S. Yang and K.L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.
  29. G.S. Yang and M.C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37.
  30. M. E. Yıldırım, A. Akkurt and Yıldırım, Hermite-Hadamard type inequalities for co-ordinated (α1;m1) -(α2;m2)-convex functions via fractional integrals, Contemporary Analysis and Applied Mathematics, 4(1), 48-63, 2016.
  31. H. P. Yin, F. Qi, Hermite-Hadamard type inequalities for the product of (α;m)-convex functions, J. Nonlinear Sci. Appl. 8 (2015) 231-236.
  32. M.E. Ozdemir, C. Yildiz and A.O. Akdemir, On the co-ordinated convex functions Appl. Math. Inf. Sci. 8(3), 1085-1091 (2014). Z. Pavic, Improvements of the Hermite-Hadamard inequality, Journal of Inequalities and Applications (2015) 2015:222