Abstract
This paper is devoted to the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both the mapping and the constraint set are perturbed by different parameters. By using the properties of recession cones, several equivalent characterizations are given for the set-valued vector equilibrium problems to have nonempty and bounded solution sets. As an application, the stability of solution set for the set-valued vector equilibrium problem in a reflexive Banach space is also given. The results presented in this paper generalize and extend some known results in Fan and Zhong (2008), He (2007), and Zhong and Huang (2010).
Highlights
Let X and Y be reflexive Banach spaces
Zhong and Huang 40 studied the stability analysis for a class of Minty mixed variational inequalities in reflexive Banach spaces, when both the mapping and the constraint set are perturbed. They got a stability result for the Minty mixed variational inequality with Φ-pseudomonotone mapping in a reflexive Banach space, when both the mapping and the constraint set are perturbed by different parameters, which generalized and extended some known results in 38, 39
Inspired and motivated by the works mentioned above, in this paper, we further study the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both the mapping and the constraint set are perturbed
Summary
Let X and Y be reflexive Banach spaces. Let K be a nonempty closed convex subset of X. Adly et al , and Addi et al discussed the stability of the solution set of a so-called semicoercive variational inequality He studied the stability of variational inequality problem with either the mapping or the constraint set perturbed in reflexive Banach spaces. Zhong and Huang 40 studied the stability analysis for a class of Minty mixed variational inequalities in reflexive Banach spaces, when both the mapping and the constraint set are perturbed. Inspired and motivated by the works mentioned above, in this paper, we further study the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both the mapping and the constraint set are perturbed.
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