Study on differentiability problems of interval-valued functions

The Journal of Nonlinear Sciences and its Applications

Eer-DunBai¹  Yu-E Bao²  Jin-Jun Li² 

[1] College of Computer Science and Technology, Inner Mongolia Universities, Tongliao, InnerMongolia 028043, P. R. China;College of Mathematics, Inner Mongolia University for Nationalities, Tongliao,Inner Mongolia 028043, P. R. China

关键词: Hukuhara difference;    Hausdorff distance;    interval-valued function;    \(H\)-directional differentiability;    \(D\)-directional differentiability;   

DOI  :  10.22436/jnsa.010.11.06

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

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.

【 授权许可】

Unknown