Subdifferential representation of homogeneous functions and extension of smoothness in Banach spaces |
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| Authors: | Fu Chun Yang Zhou Wei Dong Wang |
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| Affiliation: | 1. Department of Mathematics, Yunnan University, Kunming, 650091, P. R. China
2. Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville, NC, 28301, USA
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| Abstract: | In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke’s subdifferentials of locally Lipschitzian functions defined on Banach space respectively, and obtain the generalized Euler identity of homogenous functions. Then, by introducing a multifunction Γ, we extend the smoothness of sphere and differentiability of norm function in Banach space. |
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| Keywords: | Homogeneous function proximal subdifferential Clarke＇s subdifferential Euler identity smoothness |
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