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Journal of Applied Mathematics
Volume 2015, Article ID 108357, 10 pages
http://dx.doi.org/10.1155/2015/108357
Research Article

Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

1Department of Mathematics, Sichuan University, Chengdu 610064, China
2School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
3NAAM Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Received 12 August 2014; Accepted 23 September 2014

Academic Editor: Wei-Shih Du

Copyright © 2015 Wei-bing Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.