Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (6): 1732-1742.

• Articles • Previous Articles     Next Articles

Properties of the Solution in Generalized Minty Vector Variational-like Inequalities

  

  1. Department of Mathematics and Information Technology, Hanshan Normal University, Guangdong Chaozhou 521041
  • Received:2007-10-08 Revised:2008-09-16 Online:2009-12-25 Published:2009-12-25
  • Supported by:

    国家自然科学基金(60574075)资助

Abstract:

Generalized Minty vector variational-like inequalities as being of lower Dini directional derivative type are studied in topological vector  spaces, which include Minty variational inequalities, Minty  variational-like inequalities and Minty vector variational inequalities as being of differential type. Some relations between solutions of Minty vector
variational-like inequalities and solutions of vector optimization problems, as well as radial decrease properties of functions, are investigated. Moreover, the affine solution sets of Minty  vector variational-like inequalities  are
presented. As consequences, some recent known results in literature are obtained in the special case.

Key words: Vector variational-like inequality, Invex set, Invex function, Radial decrease function

CLC Number: 

  • 49J20
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