# Study on differentiability problems of interval-valued functions

Volume 10, Issue 11, pp 5677--5689

Publication Date: 2017-11-10

http://dx.doi.org/10.22436/jnsa.010.11.06

### Authors

Yu-E Bao - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. China
Jin-Jun Li - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. China
Eer-Dun Bai - College of Computer Science and Technology, Inner Mongolia Universities, Tongliao, Inner Mongolia 028043, P. R. China

### Abstract

In this paper, we give the concepts of $H$-directional differentiability and $D$-directional differentiability of interval-valued functions. Then we discuss the properties of $H$-directional differentiable interval-valued functions and $D$-directional differentiable interval-valued functions. The necessary and sufficient conditions for the $H$-directional differentiability are given together with the sufficient conditions and the necessary and sufficient conditions for $D$-directional differentiability of interval-valued functions. Then we discuss the relationship between the two directional differentiability and prove these directional differentiability can be equivalent under a certain conditions.

### Keywords

Hukuhara difference, Hausdorff distance, interval-valued function, $H$-directional differentiability, $D$-directional differentiability