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Systems of Vector Quasi-equilibrium Problems and Their Applications

  • Qamrul Hasan Ansari
  • Jen-Chih Yao
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 47)

Abstract

In this survey chapter, we present systems of various kinds of vector quasi-equilibrium problems and give existence theory for their solutions. Some applications to systems of vector quasi-optimization problems, quasi-saddle point problems for vector-valued functions and Debreu type equilibrium problems, also known as constrained Nash equilibrium problems, for vector-valued functions are presented. The investigations of this chapter are based on our papers: Ansari (J Math Anal Appl 341:1271–1283, 2008); Ansari et al. (J Global Optim 29:45–57, 2004); Ansari and Khan (Mathematical Analysis and Applications, edited by S. Nanda and G.P. Rajasekhar, Narosa, New Delhi, 2004, pp.1–13); and Ansari et al. (J Optim Theory Appl 127:27–44, 2005).

Keywords

Equilibrium Problem Topological Vector Space Vector Variational Inequality Vector Equilibrium Problem Nash Equilibrium Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

Authors are grateful to the referees for their valuable comments and suggestions.

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan

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