Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (6): 1080-1088.

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QCLkR Spaces and QCLkS Spaces

Zeng Chaoying1, Suyalatu2   

  1. 1 The Department of Mathematics, Ji Ning Normal College, Inner Mongolia Wulanchabu 012000;
    2 The College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022
  • Received:2015-04-16 Revised:2015-10-01 Online:2015-12-25 Published:2015-12-25

Abstract:

In this article, we introduce the concepts of QCLkR spaces and QCLkS spaces and show that QCLkR spaces and QCLkS spaces are dual concepts by using the local reflexive principle. Also, we give some characteristic descriptions of QCLkR spaces and QCLkS spaces by using the slice of unit ball, and discuss the relation between QCLkR spaces, QCLkS spaces with other convexity and smoothness. The results perfect the research on convexity and smoothness about Banach spaces.

Key words: QCLkR space, QCLkS space, Local reflexive principle, Banach space

CLC Number: 

  • O177.2
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