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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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