Generalizations of Several Inequalities Related to Multivariate Geometric Means

Abstract

In the paper, by some methods in the theory of majorization, the authors generalize several inequalities related to multivariate geometric means.

On HT-convexity and Hadamard-type inequalities

“…In this section, we will consider applications of our newly-established results to the following special means. For real numbers τ , μ > 0, the arithmetic mean and the p-logarithmic mean are respectively defined [26,29]…”

Some new integral inequalities of the Simpson type for MT-convex functions

“…Due to wide applications of various convex functions, some mathematicians have dedicated to studying integral inequalities of the HermiteHadamard type for dierent classes of convex functions. For details, please refer to [1,3,5,12,16,17,18,19,20,21,22,23] and closely related references therein.…”