Year: 2010
Author: Shaorong Pan, Hongwei Zhang, Liwei Zhang
Communications in Mathematical Research , Vol. 26 (2010), Iss. 1 : pp. 41–52
Abstract
Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionally differentiable functions are derived. Furthermore, the mean-value theorem for a directionally differentiable function is demonstrated.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-CMR-19176
Communications in Mathematical Research , Vol. 26 (2010), Iss. 1 : pp. 41–52
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: The space of star-shaped sets gauge function isometrical isomorphism directionally differentiable function star-shaped differential mean-value theorem.