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Hermite-Hadamard-Fejér inequalities for double integrals

Year 2021, Volume: 70 Issue: 1, 100 - 116, 30.06.2021

Hüseyin Budak Mehmet Zeki Sarıkaya

https://doi.org/10.31801/cfsuasmas.748013
Cited By: 2

Abstract

In this paper, we first obtain Hermite-Hadamard-Fejer inequalities for co-ordinated convex functions in a rectangle from the plane R2. 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.

Keywords

Hermite-Hadamard-Fejer inequalities co-ordinated convex integral inequalities

References

  • 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).
  • M. Alomari and M. Darus, Fejér inequality for double integrals, Facta Universitatis (NIS), Ser. Math. Inform. 24 (2009), 15-28.
  • 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).
  • A.G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28 (1994), 7-12.
  • 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.
  • F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal., 8(4), (2014), 915-923.
  • 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).
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • S.S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones J. Math. 37(4), 343–341 (2015).
  • S.S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.
  • S.S. Dragomir, J.Pecaric, L.E. Persson, Some inequalities of Hadamard type. Soochow J. Math. 21, 335-341 (1995).
  • 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.
  • L. Fejer, Über die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369-390. (Hungarian).
  • 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.
  • 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.
  • M. A. latif, On some Fejer-type inequalities for double integrals, Tamkang Journal of Mathematics, 43(3), 2012, 423-436.
  • 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.
  • 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.
  • M. A. Latif and S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 2012, (2012): 28.
  • 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
  • J. E. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • 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.
  • 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.
  • K. L. Tseng and S. R. Hwang, New Hermite-Hadamard inequalities and their applications, Filomat, 30(14), 2016, 3667-3680.
  • 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).
  • 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).
  • 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
  • G. S. Yang and K.L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.
  • G.S. Yang and M.C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37.
  • 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.
  • 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.

Year 2021, Volume: 70 Issue: 1, 100 - 116, 30.06.2021

Hüseyin Budak Mehmet Zeki Sarıkaya

https://doi.org/10.31801/cfsuasmas.748013
Cited By: 2

Abstract

References

  • 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).
  • M. Alomari and M. Darus, Fejér inequality for double integrals, Facta Universitatis (NIS), Ser. Math. Inform. 24 (2009), 15-28.
  • 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).
  • A.G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28 (1994), 7-12.
  • 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.
  • F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal., 8(4), (2014), 915-923.
  • 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).
  • S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • S.S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones J. Math. 37(4), 343–341 (2015).
  • S.S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.
  • S.S. Dragomir, J.Pecaric, L.E. Persson, Some inequalities of Hadamard type. Soochow J. Math. 21, 335-341 (1995).
  • 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.
  • L. Fejer, Über die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369-390. (Hungarian).
  • 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.
  • 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.
  • M. A. latif, On some Fejer-type inequalities for double integrals, Tamkang Journal of Mathematics, 43(3), 2012, 423-436.
  • 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.
  • 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.
  • M. A. Latif and S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 2012, (2012): 28.
  • 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
  • J. E. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • 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.
  • 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.
  • K. L. Tseng and S. R. Hwang, New Hermite-Hadamard inequalities and their applications, Filomat, 30(14), 2016, 3667-3680.
  • 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).
  • 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).
  • 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
  • G. S. Yang and K.L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.
  • G.S. Yang and M.C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37.
  • 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.
  • 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.
There are 31 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Hüseyin Budak 0000-0001-8843-955X

Mehmet Zeki Sarıkaya 0000-0002-6165-9242

Publication Date June 30, 2021
Submission Date June 4, 2020
Acceptance Date October 9, 2020
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA 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, 70(1), 100-116. https://doi.org/10.31801/cfsuasmas.748013
AMA Budak H, Sarıkaya MZ. Hermite-Hadamard-Fejér inequalities for double integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):100-116. doi:10.31801/cfsuasmas.748013
Chicago Budak, Hüseyin, and Mehmet Zeki Sarıkaya. “Hermite-Hadamard-Fejér Inequalities for Double Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 100-116. https://doi.org/10.31801/cfsuasmas.748013.
EndNote Budak H, Sarıkaya MZ (June 1, 2021) Hermite-Hadamard-Fejér inequalities for double integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 100–116.
IEEE H. Budak and M. Z. Sarıkaya, “Hermite-Hadamard-Fejér inequalities for double integrals”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 100–116, 2021, doi: 10.31801/cfsuasmas.748013.
ISNAD Budak, Hüseyin - Sarıkaya, Mehmet Zeki. “Hermite-Hadamard-Fejér Inequalities for Double Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 100-116. https://doi.org/10.31801/cfsuasmas.748013.
JAMA Budak H, Sarıkaya MZ. Hermite-Hadamard-Fejér inequalities for double integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:100–116.
MLA Budak, Hüseyin and Mehmet Zeki Sarıkaya. “Hermite-Hadamard-Fejér Inequalities for Double Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 100-16, doi:10.31801/cfsuasmas.748013.
Vancouver Budak H, Sarıkaya MZ. Hermite-Hadamard-Fejér inequalities for double integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):100-16.

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