Research article

Fejér type inequalities for harmonically convex functions

  • Received: 07 April 2022 Revised: 08 June 2022 Accepted: 09 June 2022 Published: 16 June 2022
  • MSC : 26D15, 26D20, 26D07

  • In this study, some mappings related to the Fejér-type inequalities for harmonically convex functions are defined over $ \left[ 0, 1\right] $. Some Fejér-type inequalities for harmonically convex functions are proved using these mappings. Properties of these mappings are considered and consequently, refinements are obtained of some known results.

    Citation: Muhammad Amer Latif. Fejér type inequalities for harmonically convex functions[J]. AIMS Mathematics, 2022, 7(8): 15234-15257. doi: 10.3934/math.2022835

    Related Papers:

  • In this study, some mappings related to the Fejér-type inequalities for harmonically convex functions are defined over $ \left[ 0, 1\right] $. Some Fejér-type inequalities for harmonically convex functions are proved using these mappings. Properties of these mappings are considered and consequently, refinements are obtained of some known results.



    加载中


    [1] F. Chen, S. Wu, Fejér and Hermite-Hadamard type inequalities for harmonically convex functions, J. Appl. Math., 2014 (2014). https://doi.org/10.1155/2014/386806 doi: 10.1155/2014/386806
    [2] S. S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49–56. https://doi.org/10.1016/0022-247X(92)90233-4 doi: 10.1016/0022-247X(92)90233-4
    [3] S. S. Dragomir, A refinement of Hadamard's inequality for isotonic linear functionals, Tamkang J. Math., 24 (1993), 101–106. https://doi.org/10.5556/j.tkjm.24.1993.4479 doi: 10.5556/j.tkjm.24.1993.4479
    [4] S. S. Dragomir, On the Hadamard's inequality for convex on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5 (2001), 775–788.
    [5] S. S. Dragomir, Further properties of some mapping associated with Hermite-Hadamard inequalities, Tamkang J. Math., 34 (2003), 45–57. https://doi.org/10.5556/j.tkjm.34.2003.271 doi: 10.5556/j.tkjm.34.2003.271
    [6] S. S. Dragomir, Y. J. Cho, S. S. Kim, Inequalities of Hadamard's type for Lipschitzian mappings and their applications, J. Math. Anal. Appl., 245 (2000), 489–501. https://doi.org/10.1006/jmaa.2000.6769 doi: 10.1006/jmaa.2000.6769
    [7] S. S. Dragomir, D. S. Milŏsević, J. Sándor, On some refinements of Hadamard's inequalities and applications, Univ. Belgrad. Publ. Elek. Fak. Sci. Math., 4 (1993), 3–10.
    [8] S. S. Dragomir, Inequalities of Jensen type for HA-convex functions, Fasc. Math., 1 (2020), 103–124.
    [9] S. S. Dragomir, Inequalities of Hermite-Hadamard type for HA-convex functions, Moroccan J. Pure Appl. Anal., 3 (2017), 83–101. https://doi.org/10.1515/mjpaa-2017-0008 doi: 10.1515/mjpaa-2017-0008
    [10] S. S. Dragomir, On Hadamard's inequality for convex functions, Mat. Balkanica, 6 (1992), 215–222. https://doi.org/10.1017/S0004972700031786 doi: 10.1017/S0004972700031786
    [11] S. S. Dragomir, On Hadamard's inequality for the convex mappings defined on a ball in the space and applications, Math. Inequal. Appl., 3 (2000), 177–187. https://doi.org/10.7153/mia-03-21 doi: 10.7153/mia-03-21
    [12] S. S. Dragomir, On Hadamard's inequality on a disk, J. Inequal. Pure Appl. Math., 1 (2000).
    [13] S. S. Dragomir, On some integral inequalities for convex functions, Zb. Rad., 1996, 21–25.
    [14] S. S. Dragomir, R. P. Agarwal, Two new mappings associated with Hadamard's inequalities for convex functions, Appl. Math. Lett., 11 (1998), 33–38. https://doi.org/10.1016/S0893-9659(98)00030-5 doi: 10.1016/S0893-9659(98)00030-5
    [15] L. Fejér, Über die fourierreihen Ⅱ, Math. Naturwiss. Anz Ungar. Akad. Wiss, 24 (1906), 369–390.
    [16] J. Hadamard, Étude sur les propriétés des fonctions entières en particulier d'une function considérée par Riemann, J. Math. Pures Appl., 58 (1983), 171–215.
    [17] İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (2014), 935–942.
    [18] M. I. Ho, Fejer inequalities for Wright-convex functions, J. Inequal. Pure Appl. Math., 8 (2007).
    [19] D. Y. Hwang, K. L. Tseng, G. S. Yang, Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese J. Math., 11 (2007), 63–73. https://doi.org/10.11650/twjm/1500404635 doi: 10.11650/twjm/1500404635
    [20] K. C. Lee, K. L. Tseng, On a weighted generalization of Hadamard's inequality for Gconvex functions, Tamsui-Oxford J. Math. Sci., 16 (2000), 91–104.
    [21] M. A. Latif, Mappings related to Hermite-Hadamard type inequalities for harmonically convex functions (Submitted).
    [22] M. A. Latif, S. S. Dragomir, E. Momoniat. Fejér type inequalities for harmonically-convex functions with applications, J. Appl. Anal. Comput., 7 (2017), 795–813. https://doi.org/10.11948/2017050 doi: 10.11948/2017050
    [23] K. L. Tseng, S. R. Hwang, S. S. Dragomir, On some new inequalities of Hermite-Hadamard-Fejér type involving convex functions, Demonstr. Math., 40 (2007), 51–64. https://doi.org/10.1515/dema-2007-0108 doi: 10.1515/dema-2007-0108
    [24] K. L. Tseng, S. R. Hwang, S. S. Dragomir, Fejér-type inequalities (Ⅰ), J. Inequal. Appl., 2010 (2010), 531976. https://doi.org/10.1155/2010/531976 doi: 10.1155/2010/531976
    [25] K. L. Tseng, S. R. Hwang, S. S. Dragomir, Fejér-type inequalities (Ⅱ), RGMIA Res. Rep. Coll., 12 (2009), 1–12.
    [26] R. Xiang, Refinements of Hermite-Hadamard type inequalities for convex functions via fractional integrals, J. Appl. Math. Inform., 33 (2015), 119–125. https://doi.org/10.14317/jami.2015.119 doi: 10.14317/jami.2015.119
    [27] G. S. Yang, M. C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33–37. https://doi.org/10.5556/j.tkjm.28.1997.4331 doi: 10.5556/j.tkjm.28.1997.4331
    [28] G. S. Yang, K. L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180–187. https://doi.org/10.1006/jmaa.1999.6506 doi: 10.1006/jmaa.1999.6506
    [29] G. S. Yang, K. L. Tseng, Inequalities of Hadamard's type for Lipschitzian mappings, J. Math. Anal. Appl., 260 (2001), 230–238. https://doi.org/10.1006/jmaa.2000.7460 doi: 10.1006/jmaa.2000.7460
    [30] G. S. Yang, K. L. Tseng, On certain multiple integral inequalities related to Hermite-Hadamard inequalities, Utilitas Math., 62 (2002), 131–142.
    [31] G. S. Yang, K. L. Tseng, Inequalities of Hermite-Hadamard-Fejér type for convex functions and Lipschitzian functions, Taiwanese J. Math., 7 (2003), 433–440.
  • Reader Comments
  • © 2022 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(223) PDF downloads(47) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog