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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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