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

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