Geodesic
Well-posedness for a class of strong vector equilibrium problems
Yanlong, Yang1 ; Xicai, Deng2 ; Shuwen, Xiang1 ; Wensheng, Jia1
1 School of computer science and technology, Guizhou University, Guiyang 550025, China
2 Department of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 84-91.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.01.08
Classification : 49K40, 90C31
Keywords: Strong vector equilibrium problems, well-posedness, dense set, metric characterizations.

Yanlong, Yang 1 ; Xicai, Deng 2 ; Shuwen, Xiang 1 ; Wensheng, Jia 1

1 School of computer science and technology, Guizhou University, Guiyang 550025, China
2 Department of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, China 
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Yanlong, Yang; Xicai, Deng; Shuwen, Xiang; Wensheng, Jia. Well-posedness for a class of strong vector equilibrium problems. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 84-91. doi : 10.22436/jnsa.010.01.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.08/

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