Study on differentiability problems of interval-valued functions

Volume 10, Issue 11, pp 5677--5689 http://dx.doi.org/10.22436/jnsa.010.11.06

Publication Date: November 10, 2017 Submission Date: January 24, 2017

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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.

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ISRP Style

Yu-E Bao, Jin-Jun Li, Eer-Dun Bai, Study on differentiability problems of interval-valued functions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5677--5689

AMA Style

Bao Yu-E, Li Jin-Jun, Bai Eer-Dun, Study on differentiability problems of interval-valued functions. J. Nonlinear Sci. Appl. (2017); 10(11):5677--5689

Chicago/Turabian Style

Bao, Yu-E, Li , Jin-Jun, Bai, Eer-Dun. "Study on differentiability problems of interval-valued functions." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5677--5689

Keywords

Hukuhara difference
Hausdorff distance
interval-valued function
\(H\)-directional differentiability
\(D\)-directional differentiability

MSC

46T20
46G05

References

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