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Journal of Global Optimization

, Volume 43, Issue 1, pp 23–45 | Cite as

Generalizations of vector quasivariational inclusion problems with set-valued maps

  • Pham Huu SachEmail author
  • Le Anh Tuan
Article

Abstract

Existence theorems are given for the problem of finding a point (z 0,x 0) of a set E × K such that \((z_0,x_0)\in B(z_0,x_0)\times A(z_0,x_0)\) and, for all \(\eta\in A(z_0,x_0), (F(z_0,x_0,x_0,\eta), C(z_0,x_0,x_0,\eta))\in \alpha\) where α is a relation on 2 Y (i.e., a subset of 2 Y  × 2 Y ), \(A : E\times K\longrightarrow 2^K,\) \(B : E\times K\longrightarrow 2^E, C : E\times K\times K\times K\longrightarrow 2^Y\) and \(F : E\times K\times K\times K\longrightarrow 2^Y\) are some set-valued maps, and Y is a topological vector space. Detailed discussions are devoted to special cases of α and C which correspond to several generalized vector quasi-equilibrium problems with set-valued maps. In such special cases, existence theorems are obtained with or without pseudomonotonicity assumptions.

Keywords

Quasivariational inclusion problem Set-valued map Existence theorem Pseudomonotonicity Generalized concavity 

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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Hanoi Institute of MathematicsHanoiVietnam
  2. 2.Ninh Thuan College of PedagogyNinh ThuanVietnam

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