A Collection of inequalities involving the logarithmic function

Kyriakis, Alexandros

doi:10.21608/ejmaa.2025.414122.1374

A Collection of inequalities involving the logarithmic function

Document Type : Regular research papers

Author

Alexandros Kyriakis

Boston College UK, Department of Mathematics and Engineering

10.21608/ejmaa.2025.414122.1374

Abstract

The main topic of this article is the derivation of interpolation inequalities involving logarithmic functions. There are eight inequalities presented in this manuscript which involve logarithmic functions of a single real variable. The results are novel and the approach taken to obtain the results relies purely on functional inequalities and not on monotonicity properties or series expansions as other works in the literature. Logarithmic functions are ubiquitous in Mathematics, and one could think of Analytic Number Theory where these class of functions appears a lot. It is a contemporary research area to find appropriate estimates, and this work was strongly motivated and intensely infuenced by the works of Bagul-Chesneau and Kostic. This article demonstrates the elegance of integral inequalities, and using these integral inequalities in a smart way enables to generate logarithmic inequalities avoiding the computational challenges that the monotonicity approach imposes. All the results have been rigorously proved theoretically and there are graphical demonstrations that verify the theory behind the obtained inequalities.

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