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On some curves in vector lattices. (English) Zbl 0881.46006
Concave $$\varepsilon$$-convex mappings $$F$$ from an interval $$I$$ on the real line into a boundedly complete vector lattice $$(X,\preceq)$$ with $$0 \preceq \varepsilon \in X$$ are investigated. Affine functions $$a : I \to X$$ separating $$F$$ and $$F + \varepsilon$$ are constructed. Extension theorems for concave mappings are also formulated. Some of the results are obtained under the additional assumption that $$X$$ is a Banach lattice.
##### MSC:
 46A40 Ordered topological linear spaces, vector lattices 26D07 Inequalities involving other types of functions 46B42 Banach lattices 26A51 Convexity of real functions in one variable, generalizations
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