Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (3): 1035-1040.doi: 10.1016/S0252-9602(11)60295-6

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NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OFU-CONVEXITY IN BANACH SPACES

 Ji Gao, Satit Saejung*   

  1. Department of Mathematics, Community College of Philadelphia, Philadelphia, PA 19130-3991, USA|Department of Mathematics, Faculty of Science, Khon Kaen University, |Khon Kaen 40002, Thailand
  • Received:2009-02-05 Revised:2009-10-14 Online:2011-05-20 Published:2011-05-20
  • Contact: Satit Saejung E-mail:jgao@ccp.edu; saejung@kku.ac.th

Abstract:

We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters 
UaX(ε) and βX(ε), both related to Gao's modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.

Key words: uniform normal structure, modulus of convexity, ultrapower

CLC Number: 

  • 46B20
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