The uniqueness and well-posedness of vector equilibrium problems with a representation theorem for the solution set
Dingtao Peng, Jian Qiao Yu, Naihua Xiu · Fixed Point Theory and Applications · 2014
This paper aims to present some uniqueness and well-posedness results for vector equilibrium problems (for short, VEPs). We first construct a complete metric space M consisting of VEPs satisfying some conditions. Using the method of set-valued analysis, we prove that there exists a dense everywhere residual subset Q of M 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 in M . MSC: 49K40, 90C31, 46B40, 47H04.