Research article

On Fejer type inequalities for co-ordinated hyperbolic ρ-convex functions

  • Received: 27 November 2019 Accepted: 21 May 2020 Published: 27 May 2020
  • MSC : 26D07, 26D10, 26D15, 26A33

  • In this study, we first establish some Hermite-Hadamard-Fejer type inequalities for coordinated hyperbolic ρ-convex functions. Then, by utilizing these inequalities, we also give some fractional Fejer type inequalities for co-ordinated hyperbolic ρ-convex functions. The inequalities obtained in this study provide generalizations of some result given in earlier works.

    Citation: Hasan Kara, Hüseyin Budak, Mehmet Eyüp Kiriş. On Fejer type inequalities for co-ordinated hyperbolic ρ-convex functions[J]. AIMS Mathematics, 2020, 5(5): 4681-4701. doi: 10.3934/math.2020300

    Related Papers:

  • In this study, we first establish some Hermite-Hadamard-Fejer type inequalities for coordinated hyperbolic ρ-convex functions. Then, by utilizing these inequalities, we also give some fractional Fejer type inequalities for co-ordinated hyperbolic ρ-convex functions. The inequalities obtained in this study provide generalizations of some result given in earlier works.


    加载中


    [1] A. Akkurt, M. Z. Sarikaya, H. Budak, et al. On the Hadamard's type inequalities for co-ordinated convex functions via fractional integrals, Journal of King Saud University - Science, 29 (2017), 380-387. doi: 10.1016/j.jksus.2016.06.003
    [2] T. Ali, M. A. Khan, A. Kilicman, et al. On the refined Hermite-Hadamard inequalities, Mathematical Sciences & Applications E-Notes, 6 (2018), 85-92.
    [3] A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28 (1994), 7-12.
    [4] M. K. Bakula, An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates, Australian journal of mathematical analysis and applications, 11 (2014), 1-7.
    [5] H. Budak and M. Z. Sarikaya, Hermite-Hadamard-Fejer inequalities for double integrals, submitted, 2018.
    [6] F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal., 8 (2014), 915-923.
    [7] F. Chen, A note on Hermite-Hadamard inequalities for products of convex functions, J. Appl. Math., 2013 (2013), 935020.
    [8] F. Chen, S. Wu, Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 705-716. doi: 10.22436/jnsa.009.02.32
    [9] S. S. Dragomir and C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
    [10] S. S. Dragomir, Some inequalities of Hermite-Hadamard type for hyperbolic ρ-convex functions, Preprint, 2018.
    [11] S. S. Dragomir, On Hadamards inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwan J. Math., 4 (2001), 775-788.
    [12] S. S. Dragomir, Some inequalities of Fejer type for hyperbolic ρ-convex functions, Preprint, 2018.
    [13] S. S. Dragomir, Some inequalities of Ostrowski and trapezoid type for hyperbolic ρ-convex functions, Preprint, 2018.
    [14] S. S. Dragomir, Some inequalities of Jensen type for hyperbolic ρ-convex functions, Preprint, 2018.
    [15] S. S. Dragomir and B. T. Torebek, Some Hermite-Hadamard type inequalities in the class of hyperbolic ρ-convex functions, arXiv preprint, arXiv:1901.06634, 2019.
    [16] G. Farid, M. Marwan and A. U. Rehman, Fejer-Hadamard inequlality for convex functions on the co-ordinates in a rectangle from the plane, International Journal of Analysis and Applications, 10 (2016), 40-47.
    [17] L. Fejer, Über die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369-390. (Hungarian)
    [18] J. Hadamard, Etude sur les proprietes des fonctions entieres en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
    [19] U. S. Kırmacı, M. K. Bakula, M. E. Özdemir, et al. Hadamard-tpye inequalities for s-convex functions, Appl. Math. Comput., 193 (2007), 26-35.
    [20] M. A. Latif and M. Alomari, Hadamard-type inequalities for product two convex functions on the co-ordinetes, Int. Math. Forum, 4 (2009), 2327-2338.
    [21] M. A. Latif, S. S. Dragomir, E. Momoniat, Generalization of some Inequalities for differentiable co-ordinated convex functions with applications, Moroccan J. Pure Appl. Anal., 2 (2016), 12-32. doi: 10.7603/s40956-016-0002-4
    [22] M. A. Latif and S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 2012 (2012), 28.
    [23] K. Ozcelik, H. Budak, S. S. Dragomir, On Hermite-Hadamard type inequalities for co-ordinated hyperbolic ρ-convex functions, Submitted, 2019.
    [24] M. E. Ozdemir, C. Yildiz and A. O. Akdemir, On the co-ordinated convex functions, Appl. Math. Inf. Sci., 8 (2014), 1085-1091. doi: 10.12785/amis/080318
    [25] B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll, 6 (2003), 1-9.
    [26] Z. Pavic, Improvements of the Hermite-Hadamard inequality, J. Inequal. Appl., 2015 (2015), 1-11. doi: 10.1186/1029-242X-2015-1
    [27] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
    [28] M. Z. Sarikaya, E. Set, M. E. Ozdemir, et al.New some Hadamard's type inequalities for coordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28 (2012), 137-152.
    [29] M. Z. Sarikaya, On the Hermite-Hadamard-type inequalities for co-ordinated convex functions via fractional integrals, Integ. Transf. Spec. F., 25 (2014), 134-147. doi: 10.1080/10652469.2013.824436
    [30] E. Set, M. E. Özdemir, S. S. Dragomir, On the Hermite-Hadamard inequality and other integral inequalities involving two functions, J. Inequal. Appl., 2010 (2010), 148102.
    [31] K. L. Tseng and S. R. Hwang, New Hermite-Hadamard inequalities and their applications, Filomat, 30 (2016), 3667-3680. doi: 10.2298/FIL1614667T
    [32] 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 (2007), 63-73. doi: 10.11650/twjm/1500404635
    [33] R. Xiang and F. Chen, On some integral inequalities related to Hermite-Hadamard-Fejér inequalities for coordinated convex functions, Chinese Journal of Mathematics, 2014 (2014), 796132.
    [34] H. Yaldız, M. Z. Sarikaya, Z. Dahmani, On the Hermite-Hadamard-Fejer-type inequalities for coordinated convex functions via fractional integrals, An International Journal of Optimization and Control: Theories & Applications, 7 (2017), 205-215.
    [35] G. S. Yang and K. L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187. doi: 10.1006/jmaa.1999.6506
    [36] G. S. Yang and M. C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3307) PDF downloads(288) Cited by(1)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog