A note on h-convex functions
Authors: Mohammad W. Alomari
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2019 · Pages: 55 - 67
Published Online: 16 Dec 2019
Abstract: In this work, we discuss the continuity of h-convex functions by introducing the concepts of h-convex curves (h-cord). Geometric interpretation of h-convexity is given. The fact that for a h-continuous function f, is being h-convex if and only if is h-midconvex is proved. Generally, we prove that if f is h-convex then f is h-continuous. A discussion regarding derivative characterization of h-convexity is also proposed.
Keywords: h-Convex function, Hölder continuous