Well-posedness for a class of strong vector equilibrium problems
Yang Yanlong, Deng Xicai, Xiang Shu-wen, Jia Wensheng · The Journal of Nonlinear Sciences and Applications · 2017
In this paper, we first construct a complete metric space \(\Lambda\) consisting of a class of strong vector equilibrium problems (for short, (SVEP)) satisfying some conditions. Under the abstract framework, we introduce a notion of well-posedness for the (SVEP), which unifies its Hadamard and Tikhonov well-posedness. Furthermore, we prove that there exists a dense \(G_{\delta}\) set Q of \(\Lambda\) such that each (SVEP) in Q is well-posed, that is, the majority (in Baire category sense) of (SVEP) in \(\Lambda\) is well-posed. Finally, metric characterizations on the well-posedness for the (SVEP) are given.