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The generalized projection operator on reflexive Banach spaces and its applications. (English) Zbl 1129.47043
Summary: We extend the definition of the generalized projection operator $$\pi_K:B^{\ast}\to K$$, where $$B$$ is a reflexive Banach space with dual space $$B^{\ast}$$ and $$K$$ is a nonempty, closed and convex subset of $$B$$, and we study its properties and applications to solving variational inequalities.

##### MSC:
 47H10 Fixed-point theorems 46B20 Geometry and structure of normed linear spaces 47J20 Variational and other types of inequalities involving nonlinear operators (general) 49J40 Variational inequalities
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##### References:
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