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Existence of Solutions for Generalized Vector Quasi‐Equilibrium Problems by Scalarization Method with Applications

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  • De-ning Qu
  • Cao-zong Cheng

Abstract

The aim of this paper is to study generalized vector quasi‐equilibrium problems (GVQEPs) by scalarization method in locally convex topological vector spaces. A general nonlinear scalarization function for set‐valued mappings is introduced, its main properties are established, and some results on the existence of solutions of the GVQEPs are shown by utilizing the introduced scalarization function. Finally, a vector variational inclusion problem is discussed as an application of the results of GVQEPs.

Suggested Citation

  • De-ning Qu & Cao-zong Cheng, 2013. "Existence of Solutions for Generalized Vector Quasi‐Equilibrium Problems by Scalarization Method with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:916089
    DOI: 10.1155/2013/916089
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    References listed on IDEAS

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    1. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    2. Sehie Park & Byung-Soo Lee & Gue Myung Lee, 1998. "A general vector-valued variational inequality and its fuzzy extension," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 21, pages 1-6, January.
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