Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (2): 364-372.

• Articles • Previous Articles     Next Articles

Fixed Points and Variational Inequalities |with Lower and Upper Bounds in Topological Spaces

 PIAO Yong-Jie   

  1. Department of Mathematics, College of Science, Yanbian University, Jilin Yanji 133002
  • Received:2010-10-12 Revised:2011-09-02 Online:2012-04-25 Published:2012-04-25
  • Supported by:

    吉林省教育厅科研项目(吉教科合字[2011]第434号)资助

Abstract:

Based on an KKM type theorem and a Fan-Browder type fixed point theorem on generalized convex space, some new fixed point theorems for  a Φ-map and a weak Φ-map defined on topological spaces without any convex and linear structure and any compact setting are obtained. As applications, some existence problems of solutions for variational inequalities with lower and upper bounds were discussed in non-compact topological spaces.

Key words: Generalized convex space, KKM map,  ω-connected,  Φ-map, Weak Φ-map, Variational inequality

CLC Number: 

  • 47H10
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