Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (4): 1036-1044.

• Articles • Previous Articles     Next Articles

Section Theorems and Their Applications to Variational Inequalities on Generalized Convex Spaces

 PIAO Yong-Jie   

  1. Department of Mathematics, College of Science, Yanbian University, Jilin Yanji 133002
  • Received:2009-10-08 Revised:2010-11-06 Online:2011-08-25 Published:2011-08-25
  • Supported by:

    吉林省教育厅自然科学基金(2011[434])资助

Abstract:

The KKM type theorem on generalized convex spaces is introduced, and from which, an analytic alternative type theorem of section problem is obtained. As applications of  the above results,  the existence problems of solution for variational inequalities on generalized convex spaces are discussed. The main results of this paper improve and generalize the corresponding results in recent literatures.

Key words: Generalized convex space,   Γ-convex subset,  Γ-convex function, Upper[resp. lower] semicontinuous, KKM map, Transfer closed valued

CLC Number: 

  • 47H02
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