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@article{55701,
author = {Ramík, Jaroslav and Ghosh, Debdas},
article_location = {Amsterodam, Netherlands},
article_number = {23},
doi = {http://dx.doi.org/10.1007/s00500-021-06251-w},
keywords = {Interval valued functions; Upper gH Clarke derivative; Sublinear IVF; gH Lipschitz function;},
language = {eng},
issn = {1432-7643},
journal = {Soft Computing},
title = {Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties},
url = {https://link.springer.com/article/10.1007%2Fs00500-021-06251-w/metrics},
volume = {2021},
year = {2021}
}
TY - JOUR
ID - 55701
AU - Ramík, Jaroslav - Ghosh, Debdas
PY - 2021
TI - Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties
JF - Soft Computing
VL - 2021
IS - 23
SP - 14629-14643
EP - 14629-14643
PB - Elsevier
SN - 14327643
KW - Interval valued functions
KW - Upper gH Clarke derivative
KW - Sublinear IVF
KW - gH Lipschitz function;
UR - https://link.springer.com/article/10.1007%2Fs00500-021-06251-w/metrics
N2 - This paper is devoted to the study of gH-Clarke derivative for interval-valued functions. To find properties of the gH-Clarke derivative, the concepts of limit superior, limit inferior, and sublinear interval-valued functions are studied in the sequel. It is proved that the upper gH-Clarke derivative of a gH-Lipschitz continuous interval-valued function (IVF) always exists. For a convex and gH-Lipschitz IVF, the upper gH-Clarke derivative is found to be identical with the gH-directional derivative. It is observed that the upper gH-Clarke derivative is a sublinear IVF. Several numerical examples are provided to support the entire study.
ER -
RAMÍK, Jaroslav a Debdas GHOSH. Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties. \textit{Soft Computing}. Amsterodam, Netherlands: Elsevier, roč.~2021, č.~23, s.~14629-14643. ISSN~1432-7643. doi:10.1007/s00500-021-06251-w. 2021.
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