TY - CHAP
T1 - A generalized quasi-equilibrium problem
AU - Balaj, Mircea
AU - O’Regan, Donal
N1 - Publisher Copyright:
© Springer Science+Business Media, LLC 2010.
PY - 2010
Y1 - 2010
N2 - In this paper, using the Kakutani–Fan–Glicksberg fixed point theorem, we obtain an existence theorem for a generalized vector quasi-equilibrium problem of the following type: for a suitable choice of the sets X, Z and V and of the mappings T:X ⊸ X, R:X ⊸ X, Q:X ⊸ Z, F:X× X×Z ⊸ V, C:X ⊸ V, find x ∈ X such that x ∈ T(x) and (∀)y ∈ R(x), (α)z ∈ Q(x), ρ(F((x, y, z), C(x)), where ρ is a given binary relation on 2V and α is any of the quantifiers ∀, ∃. Finally, several particular cases are discussed and some applications are given.
AB - In this paper, using the Kakutani–Fan–Glicksberg fixed point theorem, we obtain an existence theorem for a generalized vector quasi-equilibrium problem of the following type: for a suitable choice of the sets X, Z and V and of the mappings T:X ⊸ X, R:X ⊸ X, Q:X ⊸ Z, F:X× X×Z ⊸ V, C:X ⊸ V, find x ∈ X such that x ∈ T(x) and (∀)y ∈ R(x), (α)z ∈ Q(x), ρ(F((x, y, z), C(x)), where ρ is a given binary relation on 2V and α is any of the quantifiers ∀, ∃. Finally, several particular cases are discussed and some applications are given.
UR - https://www.scopus.com/pages/publications/84976346934
U2 - 10.1007/978-1-4419-0158-3_15
DO - 10.1007/978-1-4419-0158-3_15
M3 - Chapter
AN - SCOPUS:84976346934
T3 - Springer Optimization and Its Applications
SP - 201
EP - 211
BT - Springer Optimization and Its Applications
PB - Springer International Publishing
ER -