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Convexity conditions and normal structure of Banach spaces
Authors:Satit Saejung
Institution:Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
Abstract:We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity. The latter result improves the known fact that every uniformly nonsquare space with the WORTH property has normal structure.
Keywords:Normal structure  F-convexity  E-convexity  O-convexity  P-convexity  WORTH property
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