Star-Shaped Differentiable Functions and Star-Shaped Differentials

Star-Shaped Differentiable Functions and Star-Shaped Differentials

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.

Author Details

Shaorong Pan

Hongwei Zhang

Liwei Zhang