Search Advanced

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 19929-19940. doi: 10.3934/mbe.2023882
Previous Article Next Article
Research article Special Issues

Weighted Hermite–Hadamard integral inequalities for general convex functions

  • 1.
    Institute of Applied Pedagogy, Juhász Gyula Faculty of Education, University of Szeged, Hattyas utca 10, H-6725 Szeged, Hungary
  • 2.
    UNNE, FaCENA, Ave. Libertad 5450, Corrientes 3400, Argentina
  • 3.
    UTN-FRRE, French 414, Resistencia, Chaco 3500, Argentina
  • 4.
    Faculty of Education, Bursa Uludag University, Gorukle Campus, 16059, Bursa, Turkey
  • Received: 09 October 2023 Revised: 25 October 2023 Accepted: 30 October 2023 Published: 02 November 2023

  • In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite–Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann–Liouville and the $ k $-Riemann–Liouville fractional integral operators. The functions for which the operators were considered satisfy various conditions such as the $ h $-convexity, modified $ h $-convexity and $ s $-convexity.

    Citation: Péter Kórus, Juan Eduardo Nápoles Valdés, Bahtiyar Bayraktar. Weighted Hermite–Hadamard integral inequalities for general convex functions[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19929-19940. doi: 10.3934/mbe.2023882

    Related Papers:

  • In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite–Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann–Liouville and the $ k $-Riemann–Liouville fractional integral operators. The functions for which the operators were considered satisfy various conditions such as the $ h $-convexity, modified $ h $-convexity and $ s $-convexity.


    加载中


    [1] J. E. Nápoles Valdés, F. Rabossi, A. D. Samaniego, Convex functions: Ariadne's thread or Charlotte's Spiderweb?, Adv. Math. Models Appl., 5 (2020), 176–191. Available from: http://jomardpublishing.com/UploadFiles/Files/journals/AMMAV1N1/V5N2/Napoles%20Valdes.pdf
    [2] S. S. Dragomir, J. Pečarić, L.-E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335–341.
    [3] W. W. Breckner, Stetigkeitsaussagen für eine klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen, Pub. Inst. Math., 23 (1978), 13–20. Available from: http://elib.mi.sanu.ac.rs/files/journals/publ/43/3.pdf
    [4] G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim. Cluj-Naploca (Romania) (1984), 329–338.
    [5] V. G. Mihesan, A generalization of convexity, Proceedings of the Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania, 1993.
    [6] S. Varošanec, On $h$-convexity, J. Math. Anal. Appl., 326 (2007), 303–311. https://doi.org/10.1016/j.jmaa.2006.02.086 doi: 10.1016/j.jmaa.2006.02.086
    [7] M. Bessenyei, Z. Páles, On generalized higher-order convexity and Hermite–Hadamard-type inequalities, Acta Sci. Math. (Szeged), 70 (2004), 13–24.
    [8] S. S. Dragomir, Inequalities of Hermite–Hadamard type for $ GA$-convex functions, Ann. Math. Sil., 32 (2018), 145–168. https://doi.org/10.2478/amsil-2018-0001 doi: 10.2478/amsil-2018-0001
    [9] S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. Available from: https://rgmia.org/papers/monographs/Master.pdf
    [10] T. S. Du, C. Y. Luo, Z. J. Cao, On the Bullen-type inequalities via generalized fractional integrals and their applications, Fractals, 29 (2021), no. 7, 2150188. https://doi.org/10.1142/S0218348X21501887 doi: 10.1142/S0218348X21501887
    [11] T. S. Du, Y. Peng, Hermite–Hadamard type inequalities for multiplicative Riemann–Liouville fractional integrals, J. Comput. Appl. Math. (2023), 115582. https://doi.org/10.1016/j.cam.2023.115582 doi: 10.1016/j.cam.2023.115582
    [12] T. S. Du, T. C. Zhou, On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings, Chaos Solitons Fractals, 156 (2022), 111846. https://doi.org/10.1016/j.chaos.2022.111846 doi: 10.1016/j.chaos.2022.111846
    [13] M. Klaričić, E. Neuman, J. Pečarić, V. Šimić, Hermite-Hadamard's inequalities for multivariate $g$-convex functions, Math. Inequal. Appl., 8 (2005), no. 2,305–316. https://doi.org/10.7153/mia-08-28 doi: 10.7153/mia-08-28
    [14] M. S. Moslehian, Matrix Hermite–Hadamard type inequalities, Houston J. Math., 39 (2013), no. 1, 177–189. Available from: arXiv:1203.5300
    [15] J. E. Nápoles Valdés, J. M. Rodríguez, J. M. Sigarreta, New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators, Symmetry, 11 (2019), 1108. https://doi.org/10.3390/sym11091108 doi: 10.3390/sym11091108
    [16] T. C. Zhou, Z. R. Yuan, T. S. Du, On the fractional integral inclusions having exponential kernels for interval-valued convex functions, Math. Sci., 17 (2023), 107–120. https://doi.org/10.1007/s40096-021-00445-x doi: 10.1007/s40096-021-00445-x
    [17] E. D. Rainville, Special Functions, Macmillan Co., New York, 1960.
    [18] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
    [19] S. Mubeen, G. M. Habibullah, $k$-Fractional Integrals and Application, Int. J. Contemp. Math. Sci., 7 (2012), no. 2, 89–94. Available from: http://m-hikari.com/ijcms/ijcms-2012/1-4-2012/mubeenIJCMS1-4-2012-1.pdf
    [20] P. O. Mohammed, M. Z. Sarıkaya, On generalized fractional integral inequalities for twice differentiable convex functions, Int. J. Comput. Appl. Math., 372 (2020), 112740. https://doi.org/10.1016/j.cam.2020.112740 doi: 10.1016/j.cam.2020.112740
    [21] M. Tomar, E. Set, M. Z. Sarıkaya, Hermite-Hadamard type Riemann-Liouville fractional integral inequalities for convex functions, AIP Conf. Proc., 1726 (2016), 020035. https://doi.org/10.1063/1.4945861 doi: 10.1063/1.4945861
    [22] B. Bayraktar, Some new generalizations of Hadamard–type Midpoint inequalities involving fractional integrals, Probl. Anal. Issues Anal., 9 (27), no. 3, (2020), 66–82. https://doi.org/10.15393/j3.art.2020.8270
    [23] M. Z. Sarıkaya, N. Aktan, On the generalization of some integral inequalities and their applications, Math. Comput. Modelling, 54 (2011), 2175 –2182. https://doi.org/10.1016/j.mcm.2011.05.026 doi: 10.1016/j.mcm.2011.05.026
    [24] M. Alomari, M. Darus, S. S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, RGMIA Res. Rep. Coll., 12 (2009), Supplement, Article 17. Available from: https://rgmia.org/papers/v12e/Correctedmdssd.pdf
  • Reader Comments
  • © 2023 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
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(1030) PDF downloads(65) Cited by(1)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog