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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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