Existence of solutions and Hadamard well-posedness for generalized strong vector quasi-equilibrium problems

Volume 9, Issue 6, pp 4104--4113 http://dx.doi.org/10.22436/jnsa.009.06.54

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Authors

Jing Zeng - College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China. Zai-Yun Peng - College of Mathematics and Statistics, School of Science, Chongqing Jiaotong University, Chongqing 400074, China. Xiang-Kai Sun - College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China. Xian-Jun Long - College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China.

Abstract

In this paper, we establish an existence result for the (GSVQEP) without assuming that the dual of the ordering cone has a weak star compact base and give an example to show our existence theorem is different from the main result of Long et al. [X. J. Long, N. J. Huang, K. L. Teo, Math. Comput. Modelling, 47 (2008), 445-451]. Furthermore, we introduce a concept of Hadamard-type well-posedness for the (GSVQEP) and establish sufficient conditions of Hadamard-type well-posedness for the (GSVQEP).

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Keywords

• Existence theorem
• Hadamard well-posedness
• fixed-point theorem
• lower semicontinuity
• naturally quasi-convexity.
• Existence theorem
• Hadamard well-posedness
• fixed-point theorem
• lower semicontinuity
• naturally quasi-convexity.

MSC

•  49J53
•  49K40
•  90C33
•  90C46

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