Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications

Volume 9, Issue 6, pp 4399--4408 http://dx.doi.org/10.22436/jnsa.009.06.80

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Authors

Wei-Bing Zhang - Department of Information and computing science, Chengdu Technological University, Chengdu, 611730, P. R. China. Wen-Yong Yan - Department of Information and computing science, Chengdu Technological University, Chengdu, 611730, P. R. China.

Abstract

In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. By virtue of the properties of \(\Gamma\)-convex and KC-map, we give some sufficient conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. As application, we show an existence theorem of solutions for the generalized semi-infinite programs with generalized symmetric vector quasi-equilibrium constraints.

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Keywords

• Abstract convex space
• generalized symmetric vector quasi-equilibrium problem
• semi-infinite program
• \(\Gamma\)-convex
• KKM mapping.

MSC

•  47J20
•  54A05

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