Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A NOTE ON THE GENERALIZED VARIATIONAL INEQUALITY WITH OPERATOR SOLUTIONS

  • Kum, Sangho (Department of Mathematics Education Chungbuk National University)
  • Received : 2009.04.21
  • Accepted : 2009.08.14
  • Published : 2009.09.30
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Abstract

In a series of papers [3, 4, 5], the author developed the generalized vector variational inequality with operator solutions (in short, GOVVI) by exploiting variational inequalities with operator solutions (in short, OVVI) due to Domokos and $Kolumb\acute{a}n$ [2]. In this note, we give an extension of the previous work [4] in the setting of Hausdorff locally convex spaces. To be more specific, we present an existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [7] within the framework of (GOVVI).

Keywords

References

  1. H. Ben-El-Mechaiekh, Fixed Points for Compact Set-Valued Maps, Questions and Answers in General Topology 10 (1992), 153–156.
  2. A. Domokos and J. Kolumban, Variational inequalities with operator solutions, J. Global Optim. 23 (2002), 99-110. https://doi.org/10.1023/A:1014096127736
  3. S. H. Kum and W. K. Kim, Generalized vector variational and quasi-variational inequalities with operator solutions, J. Global Optim. 32 (2005), 581–595.
  4. S. H. Kum, A variant of the generalized vector variational inequalities with operator solutions, Commun. Korean Math. Soc. 21 (2006), 665–673.
  5. S. H. Kum and W. K. Kim, Applications of generalized variational and quasi-variational inequalities with operator solutions in a TVS, J. Optim. Theory Appl. 133 (2007), 65–75.
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  7. S. J. Yu and J. C. Yao, On vector variational inequalities, J. Optim. Theory Appl. 89 (1996), 749-769. https://doi.org/10.1007/BF02275358