Abstract
In this paper, we study generalized strong vector quasi-equilibrium problems in topological vector spaces. Using the generalization of Fan-Browder fixed point theorem, we provide existence theorems for an extension of generalized strong vector quasi-equilibrium problems with and without monotonicity. The results in this paper generalize, extend and unify some well-known existence theorems in literature.
Highlights
1 Introduction The minimax inequalities of Fan [ ] are fundamental in proving many existence theorems in nonlinear analysis. Their equivalence to the equilibrium problems was introduced by Takahashi [, Lemma ] Blum and Oettli [ ] and Noor and Oettli [ ]
The equilibrium problem theory provides a novel and united treatment of a wide class of problems which arise in economics, finance, image reconstruction, ecology, transportation, network, elasticity and optimization
Throughout this paper, unless otherwise specified, we assume that X and Y are Hausdorff topological vector spaces, K is a nonempty convex subset of X and C is a pointed closed convex cone in Y with int C = ∅
Summary
The minimax inequalities of Fan [ ] are fundamental in proving many existence theorems in nonlinear analysis. For a more general form of vector equilibrium problem, we let A : K → K be a multivalued map with nonempty values where K denotes the family of subsets of K .
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