• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.683-695
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• 2001

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.