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Lower Semicontinuity of the Solution Map to a Parametric Generalized Variational Inequality in Reflexive Banach Spaces

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Abstract

This paper is concerned with the study of solution stability of a parametric generalized variational inequality in reflexive Banach spaces. Under the requirements that the operator of a unperturbed problem is of class (S) +  and operators under consideration are pseudo-monotone and demicontinuous, we show that the solution map of a parametric generalized variational inequality is lower semicontinuous. The obtained results are proved without conditions related to the degree theory and the metric projection.

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Correspondence to B. T. Kien.

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Kien, B.T. Lower Semicontinuity of the Solution Map to a Parametric Generalized Variational Inequality in Reflexive Banach Spaces. Set-Valued Anal 16, 1089 (2008). https://doi.org/10.1007/s11228-008-0098-4

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Keywords

  • Parametric generalized variational inequality
  • Generalized equation
  • Lower semicontinuity
  • Pseudo-monotonicity

Mathematics Subject Classifications (2000)

  • 47J20
  • 49J40
  • 49J53
  • 90C33