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

Hari M. Srivastava (), Sana Mehrez and Sergei M. Sitnik
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Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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

Mathematics, 2022, vol. 10, issue 17, 1-13

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.

Keywords: Hermite-Hadamard inequality; digamma function; trigamma function; absolutely continuous mapping; convex function; arithmetic mean; geometric mean; logarithmic mean (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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