Well-posedness for a class of strong vector equilibrium problems

Authors

Yang Yanlong - School of computer science and technology, Guizhou University, Guiyang 550025, China.
Deng Xicai - Department of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, China.
Xiang Shuwen - School of computer science and technology, Guizhou University, Guiyang 550025, China.
Jia Wensheng - School of computer science and technology, Guizhou University, Guiyang 550025, China.

Abstract

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.

Keywords

Strong vector equilibrium problems, well-posedness, dense set, metric characterizations.

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