Geodesic
Study on differentiability problems of interval-valued functions
Bao, Yu-E 1 ; Li , Jin-Jun 1 ; Bai, Eer-Dun 2
1 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. China
2 College of Computer Science and Technology, Inner Mongolia Universities, Tongliao, Inner Mongolia 028043, P. R. China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 11, p. 5677-5689.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.11.06
Classification : 46T20, 46G05
Keywords: Hukuhara difference, Hausdorff distance, interval-valued function, \(H\)-directional differentiability, \(D\)-directional differentiability

Bao, Yu-E  1 ; Li , Jin-Jun  1 ; Bai, Eer-Dun  2

1 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. China
2 College of Computer Science and Technology, Inner Mongolia Universities, Tongliao, Inner Mongolia 028043, P. R. China 
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Bao, Yu-E  ; Li , Jin-Jun  ; Bai, Eer-Dun . Study on differentiability problems of interval-valued functions. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 11, p. 5677-5689. doi : 10.22436/jnsa.010.11.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.11.06/

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