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.


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ISRP Style

Yang Yanlong, Deng Xicai, Xiang Shuwen, Jia Wensheng, Well-posedness for a class of strong vector equilibrium problems, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 84--91

AMA Style

Yanlong Yang, Xicai Deng, Shuwen Xiang, Wensheng Jia, Well-posedness for a class of strong vector equilibrium problems. J. Nonlinear Sci. Appl. (2017); 10(1):84--91

Chicago/Turabian Style

Yanlong, Yang, Xicai, Deng, Shuwen, Xiang, Wensheng, Jia. "Well-posedness for a class of strong vector equilibrium problems." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 84--91


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