Nobuo Yamashita and Masao Fukushima
	Key words:
variational inequality problem, level-boundedness, coercivity, natural residual
		Mathematices Subject Classification: 47J20, 65K10, 90C30

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	Abstract:
In this paper we consider the level-boundedness of the natural residual function for the variational inequality problem (VIP). We first introduce the concept of strong coercivity for vector-valued mappings. The strong coercivity is related to the weak coercivity of vector-valued mappings and is weaker than the strong monotonicity of mappings. We show that the natural residual function associated with VIP is level-bounded under the strong coercivity of the mapping involved in the VIP.

On the level-boundedness of the natural residual function for variational inequality problems

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Volume 1, Number 3, September 2005, pp. 625-630