Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A NOTE ON A REGULARIZED GAP FUNCTION OF QVI IN BANACH SPACES

  • Kum, Sangho (Department of Mathematics Education Chungbuk National University)
  • Received : 2014.02.14
  • Accepted : 2014.04.16
  • Published : 2014.05.15
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Abstract

Recently, Taji [7] and Harms et al. [4] studied the regularized gap function of QVI analogous to that of VI by Fukushima [2]. Discussions are made in a finite dimensional Euclidean space. In this note, an infinite dimensional generalization is considered in the framework of a reflexive Banach space. To do so, we introduce an extended quasi-variational inequality problem (in short, EQVI) and a generalized regularized gap function of EQVI. Then we investigate some basic properties of it. Our results may be regarded as an infinite dimensional extension of corresponding results due to Taji [7].

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References

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  1. A REMARK ON THE REGULARIZED GAP FUNCTION FOR IQVI vol.28, pp.1, 2015, https://doi.org/10.14403/jcms.2015.28.1.145