This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.
【分类号】
O177.3
【正文快照】
1. IntroductiollLet 0 < P 5 l be a fixed number, let X be a vector space and A a subset of X. A iscalled g-convex if for every z, y E A we have [z, yl0 C A. Where[z, y]P:= {Ax + Py: A,P 2 0, A0 + P[j = l},(x, y)fj:= Iz, yiP\{x, y}.In this paper we use cop
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