The system of generalized vector equilibrium problems with applications

  • Authors:

  • Qamrul Hasan Ansari;Siegfried Schaible;Jen-Chih Yao

  • Affiliations:

  • Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India (E-mail: qhansari@ridaonline.com)/;A.G. Anderson Graduate School of Management, University of California 92521-0203, USA (E-mail: siegfried.schaible@ucr.edu)/;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, ROC (E-mail: yaojc@math.nsysu.edu.tw)

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2002

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Abstract

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.