Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON GAP FUNCTIONS OF VARIATIONAL INEQUALITY IN A BANACH SPACE

  • Kum, Sang-Ho (Department of Applied Mathematics, Korea Maritime University) ;
  • Lee, Gue-Myung (Department of Applied Mathematics, Pukyong National University)
  • Published : 2001.05.01
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Abstract

In this paper we are concerned with theoretical properties of gap functions for the extended variational inequality problem (EVI) in a general Banach space. We will present a correction of a recent result of Chen et. al. without assuming the convexity of the given function Ω. Using this correction, we will discuss the continuity and the differentiability of a gap function, and compute its gradient formula under tow particular situations in a general Banach space. Our results can be regarded as infinite dimensional generalizations of the well-known results of Fukushima, and Zhu and Marcotte with soem modifications.

Keywords

References

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