The uniqueness and well-posedness of vector equilibrium problems with a representation theorem for the solution set
نویسندگان
چکیده
This paper aims to present some uniqueness and well-posedness results for vector equilibrium problems (for short, VEPs). We first construct a complete metric spaceM consisting of VEPs satisfying some conditions. Using the method of set-valued analysis, we prove that there exists a dense everywhere residual subset Q ofM such that each VEP in Q has a unique solution. Moreover, we introduce and obtain the generalized Hadamard well-posedness and generic Hadamard well-posedness of VEPs by considering the perturbations of both vector-valued functions and feasible sets. As an application, we provide a representation theorem for the solution set to each VEP inM. MSC: 49K40; 90C31; 46B40; 47H04
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تاریخ انتشار 2014