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

Set-Valued Analysis volume 16, pages 1089–1105 (2008)Cite this article

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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  1. Department of Information and Technology, Hanoi University of Civil Engineering, 55 Giai Phong, Hanoi, Vietnam

    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, 1089–1105 (2008). https://doi.org/10.1007/s11228-008-0098-4

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  • DOI: https://doi.org/10.1007/s11228-008-0098-4

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