# Well-posedness for a class of strong vector equilibrium problems

Volume 10, Issue 1, pp 84--91
Publication Date: January 26, 2017 Submission Date: September 14, 2016
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### 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.

### Share and Cite

##### 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

### Keywords

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

•  49K40
•  90C31

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