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The Farkas lemma of Shimizu, Aiyoshi and Katayama

Shimizu, Aiyoshi and Katayama have recently given a finite dimensional generalization of the classical Farkas Lemma. In this note we show that a result of Pshenichnyi on convex programming can be used to give a generalization of the result of Shimizu, Aiyoshi and Katayama to infinite dimensional spaces. A generalized Farkas Lemma of Glover is also obtained.