Acta mathematica scientia,Series B ›› 1995, Vol. 15 ›› Issue (2): 171-179.

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DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

Cheng Lizin, Zhang Feng   

  1. Math. Section, Dept. of Public Courses, Jianghan Petro. Inst. Shashi 434102, China
  • Received:1993-05-15 Revised:1993-09-06 Online:1995-06-25 Published:1995-06-25
  • Supported by:
    Supported by a foundation of COGC.

Abstract: Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are(weak) Asplund spaces.

Key words: convex function, differentiability, Banach space, Asplund space

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