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Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Author

Listed:
  • Shilpi Jain

    (Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India)

  • Khaled Mehrez

    (Département de Mathématiques, Facultée des sciences de Tunis, Université Tunis El Manar, Tunis 1068, Tunisia
    Dèpartement de Mathématiques, Issat Kasserine, Université de Kairouan, Kairouan 3100, Tunisia)

  • Dumitru Baleanu

    (Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Çankaya University, Balgat 0630, Turkey)

  • Praveen Agarwal

    (Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
    Department of Mathematics, Harish-Chandra Research Institute (HRI), Allahbad 211019, India)

Abstract

In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q -digamma and q -polygamma functions, respectively. As a consequence, new inequalities for the q -analogue of the harmonic numbers in terms of the q -polygamma functions are derived. Moreover, several inequalities for special means are also considered.

Suggested Citation

  • Shilpi Jain & Khaled Mehrez & Dumitru Baleanu & Praveen Agarwal, 2019. "Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:163-:d:204914
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    Cited by:

    1. Abdullah Ali H. Ahmadini & Waqar Afzal & Mujahid Abbas & Elkhateeb S. Aly, 2024. "Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems," Mathematics, MDPI, vol. 12(3), pages 1-28, January.

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