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Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 19929-19940. doi: 10.3934/mbe.2023882
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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.


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    [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
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