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Hermite-Hadamard-Type Integral Inequalities for Convex Functions and Their Applications

Author

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  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

  • Sana Mehrez

    (Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Sfax 3029, Tunisia)

  • Sergei M. Sitnik

    (Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), 85 Pobedy Street, 308015 Belgorod, Russia)

Abstract

In this paper, we establish new generalizations of the Hermite-Hadamard-type inequalities. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered. As applications, some new inequalities for the digamma function in terms of the trigamma function and some inequalities involving special means of real numbers are given. The results also include estimates via arithmetic, geometric and logarithmic means. The examples are derived in order to demonstrate that some of our results in this paper are more exact than the existing ones and some improve several known results available in the literature. The constants in the derived inequalities are calculated; some of these constants are sharp. As a visual example, graphs of some technically important functions are included in the text.

Suggested Citation

  • Hari M. Srivastava & Sana Mehrez & Sergei M. Sitnik, 2022. "Hermite-Hadamard-Type Integral Inequalities for Convex Functions and Their Applications," Mathematics, MDPI, vol. 10(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3127-:d:903232
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    Cited by:

    1. Sergei Sitnik, 2023. "Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”," Mathematics, MDPI, vol. 11(15), pages 1-7, August.

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