A Generalized Quasi-Equilibrium Problem

Mircea Balaj () and Donal O’Regan
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Mircea Balaj: University of Oradea
Donal O’Regan: National University of Ireland

Chapter Chapter 15 in Nonlinear Analysis and Variational Problems, 2010, pp 201-211 from Springer

Abstract: Abstract 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 $$\widetilde{x}$$ ∈X such that $$\widetilde{x}$$ ∈T( $$\widetilde{x}$$ ) and (∀)y∈R( $$\widetilde{x}$$ ), (α)z∈Q( $$\widetilde{x}$$ ), ρ(F(( $$\widetilde{x}$$ ,y,z), C( $$\widetilde{x}$$ )), 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.

Keywords: Topological Vector Space; Vector Variational Inequality; Vector Equilibrium Problem; Nonempty Convex; Hausdorff Topological Vector Space (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-0158-3_15

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DOI: 10.1007/978-1-4419-0158-3_15

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