A note on h-convex functions-Reference-Cited by-同舟云学术

A note on h-convex functions

Published:2019-01-01 Issue:1 Volume:2019 Page:55-67
ISSN:2544-9990
Container-title:e-Journal of Analysis and Applied Mathematics
language:en
Short-container-title:

Author:

Alomari Mohammad W.¹

Affiliation:

1. Department of Mathematics, Faculty of Science and Information Technology , Irbid National University , 2600 Irbid 21110, Jordan .

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/ejaam-2019-0004

Reference35 articles.

1. [1] M. W. Alomari, M. Darus, S. S. Dragomir and U. Kirmaci, On fractional differentiable s-convex functions, Jordan J. Math and Stat.3(1) (2010), 33–42.

2. [2] M. Bombardelli and S. Varošanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Compute. Math. Applica.58(9) (2009), 1869–1877.10.1016/j.camwa.2009.07.073

3. [3] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funk-tionen in topologischen linearen Räumen, Publ. Inst. Math.23 (1978), 13–20 (in German).

4. [4] W. W. Breckner and G. Orban, Continuity Properties of Rationally s-convex Mappings with Values in an Ordered Topological Linear Space, Babes-Bolyai University, Cluj-Napocoi, 1978.

5. [5] W. W. Breckner, Hölder-continuity of certain generalized convex functions, Optimization28 (1994), 201–209.10.1080/02331939408843915