Research Article

Some new properties of geometrically-convex functions

DOI: 10.2989/16073606.2023.2256476
Author(s): Shigeru Furuichi Nihon University, Tokyo, Japan, Nicuşor Minculete University of Braşov, Romania, Hamid Reza Moradi Islamic Azad University, Iran, Mohammad Sababheh Princess Sumaya University For Technology, Jordan,

Abstract

The class of geometrically convex functions is a rich class that contains some important functions. In this paper, we further explore this class and present many interesting new properties, including fundamental inequalities, supermultiplicative type inequalities, Jensen-Mercer inequality, integral inequalities, and refined forms. The obtained results extend some celebrated results from the context of convexity to geometric convexity, with interesting applications to numerical inequalities for the hyperbolic and exponential functions.

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