TY - JOUR
T1 - Vector Equilibrium Problems with Generalized Monotone Bifunctions
AU - Bianchi, Monica
AU - Hadjisavvas, N.
AU - Schaible, S.
PY - 1997
Y1 - 1997
N2 - A vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locally convex vector space, find x*∈K such that F(x*, y) ≮0 for all y∈K. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.
AB - A vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locally convex vector space, find x*∈K such that F(x*, y) ≮0 for all y∈K. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.
KW - Pseudomonotone bifunctions
KW - Quasimonotone bifunctions
KW - Vector equilibrium problems
KW - Pseudomonotone bifunctions
KW - Quasimonotone bifunctions
KW - Vector equilibrium problems
UR - http://hdl.handle.net/10807/163641
U2 - 10.1023/A:1022603406244
DO - 10.1023/A:1022603406244
M3 - Article
SN - 0022-3239
VL - 92
SP - 527
EP - 542
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
ER -