A note on $h$-convex functions
Classical Analysis and ODEs
2019-01-21 v1
Abstract
In this work, we discuss the continuity of -convex functions by introducing the concepts of -convex curves (-cord). Geometric interpretation of -convexity is given. The fact that for a -continuous function , is being -convex if and only if is -midconvex is proved. Generally, we prove that if is -convex then is -continuous. A discussion regarding derivative characterization of -convexity is also proposed.
Keywords
Cite
@article{arxiv.1901.06255,
title = {A note on $h$-convex functions},
author = {M. W. Alomari},
journal= {arXiv preprint arXiv:1901.06255},
year = {2019}
}
Comments
9 pages. arXiv admin note: text overlap with arXiv:1710.03418