The generalized decomposition theorem in Banach spaces and its applications |
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Authors: | Wen Song Zhengjun Cao |
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Institution: | Department of Mathematics, Harbin Normal University, Harbin 150080, PR China |
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Abstract: | In this paper, we first give a simple proof of the decomposition theorem in Alber (Field Inst. Comm. 25 (2000) 77) and then present a new decomposition of arbitrary elements in reflexive strictly convex and smooth Banach spaces. As applications of the decomposition theorem, we give the representations of the metric projection operator for some kind of closed convex sets. Finally, we provide a sufficient condition under which the generalized projection operator coincides with the metric projection operator. |
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Keywords: | Duality mapping Metric projection Generalized projection Basic variational principle Moreau decomposition theorem Generalized decomposition theorem |
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