A Collection of Inequalities Involving Power Exponential and Logarithmic Functions

Power exponential functions and logarithmic functions, are two classes of functions which are ubiquitous in Mathematical Analysis with lots of contemporary applications. In this article, interpolation type inequalities involving power exponential and logarithmic functions are derived, and the techniques applied to derive these inequalities are not the usual that somebody encounters in the literature. All the results are derived using functional estimates and popular integral inequalities such as the Chebyshev integral inequality version. Most of the authors in the literature use monotonicity properties and series expansions, whereas in the current work the inequalities are rigorously proved using predominantly functional estimates, which is a technique more encountered in Functional Analysis and PDEs. To the best of our knowledge, the inequalities are new in the literature and the methods to yield the inequalities is novel and non trivial. This work serves in dual manner, having a research and pedagogical purpose and contributes to the field of Mathematical Analysis and Inequalities.