TY - JOUR AU - Bao, Yu-E AU - Li , Jin-Jun AU - Bai, Eer-Dun PY - 2017 TI - Study on differentiability problems of interval-valued functions JO - Journal of Nonlinear Sciences and Applications SP - 5677--5689 VL - 10 IS - 11 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.11.06 DO - 10.22436/jnsa.010.11.06 ID - Bao2017 ER -