A new treatment of convex functions
Functional Analysis
2020-03-25 v1
Abstract
Convex functions have played a major role in the field of Mathematical inequalities. In this paper, we introduce a new concept related to convexity, which proves better estimates when the function is somehow more convex than another. In particular, we define what we called convexity as a generalization of convexity. Then we prove that convex functions have better estimates in certain known inequalities like the Hermite-Hadard inequality, super additivity of convex functions, the Majorization inequality and some means inequalities. Strongly related to this, we define the index of convexity as a measure of ``how much the function is convex". Applications including Hilbert space operators, matrices and entropies will be presented in the end.
Cite
@article{arxiv.2003.10892,
title = {A new treatment of convex functions},
author = {M. Sababheh and S. Furuichi and H. R. Moradi},
journal= {arXiv preprint arXiv:2003.10892},
year = {2020}
}