Hermite-Hadamard-Fejér inequalities for double integrals
Yıl 2021,
Cilt: 70 Sayı: 1, 100 - 116, 30.06.2021
Hüseyin Budak
,
Mehmet Zeki Sarıkaya
Öz
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.
Kaynakça
- 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, 775788 (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), 343341 (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), 117 (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.
Yıl 2021,
Cilt: 70 Sayı: 1, 100 - 116, 30.06.2021
Hüseyin Budak
,
Mehmet Zeki Sarıkaya
Kaynakça
- 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, 775788 (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), 343341 (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), 117 (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.