Hermite-Hadamard-type integral inequalities for convex functions and their applications
Date
2022
Authors
Srivastava, H.M.
Mehrez, Sana
Sitnik, Sergei M.
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
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.
Description
Keywords
Hermite-Hadamard inequality, digamma function, trigamma function, absolutely continuous mapping, convex function, arithmetic mean, geometric mean, logarithmic mean
Citation
Srivastava, H. M., Mehrez, S., & Sitnik, S. M. (2022). “Hermite-Hadamard-type integral inequalities for convex functions and their applications.” Mathematics, 10(17), 3127. https://doi.org/10.3390/math10173127