Existence and Hadamard Well-Posedness of Solutions to Generalized Strong Vector Quasi-Equilibrium Problems

ZENG Jing; PENG Zai-yun; ZHANG Shi-sheng

doi:10.3879/j.issn.1000-0887.2015.06.009

Volume 36 Issue 6

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ZENG Jing, PENG Zai-yun, ZHANG Shi-sheng. Existence and Hadamard Well-Posedness of Solutions to Generalized Strong Vector Quasi-Equilibrium Problems[J]. Applied Mathematics and Mechanics, 2015, 36(6): 651-658. doi: 10.3879/j.issn.1000-0887.2015.06.009

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Existence and Hadamard Well-Posedness of Solutions to Generalized Strong Vector Quasi-Equilibrium Problems

doi: 10.3879/j.issn.1000-0887.2015.06.009

¹College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China;²School of Science, Chongqing Jiaotong University, Chongqing 400074, P.R.China;³School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650224, P.R.China

Funds: The National Natural Science Foundation of China(11401058;11301571;11301570;11401487)

Received Date: 2015-02-15
Rev Recd Date: 2015-05-02
Publish Date: 2015-06-15

Abstract

Abstract

Under the conditions of naturally quasi C-convexity of -f(·,y,u) and upper (-C)-continuity of f, an auxiliary function was constructed and an existence theorem for solutions to generalized strong vector quasi-equilibrium problems (for short, GSVQEPs) was established based on a method of proof other than the traditional ones, without the assumption that the dual of the ordering cone has a weak^* compact base. Moreover, a definition of problem sequence convergence was given and the upper semi-continuity of solution set mappings was obtained under some proper conditions. Based on these results, a concept of Hadamard-type well-posedness for GSVQEPs was introduced and the sufficient conditions for that Hadamard well-posedness was proposed.
- generalized strong vector quasi-equilibrium problem,
- existence theorem for solutions,
- Hadamard well-posedness,
- naturally quasi C-convex

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References(15)

References

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