Acta mathematica scientia,Series A ›› 2004, Vol. 24 ›› Issue (1): 116-122.

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Approximation of Convex Functions on the Dual Spaces

 RUAN Ying-Ban, CHEN Shao-Xiong   

  • Online:2004-02-25 Published:2004-02-25
  • Supported by:

    国家自然科学基金和福建省教育委员会基金资助

Abstract:

In this paper, the authors prove that for every w^* lower semicontinuous Lipschitzian convex function on the dual of a bistrictly convexifiable Banach space can be uniformly approximated by a  sequence of w^* lower semicontinuous monotone nondecreasing Lipschitzian convex function with the dense very smooth point  set.

Key words: Convex function, Very smooth point, Gateaux differentiability, Approximation.

CLC Number: 

  • 46B20
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