Geodesic
An analogue of the Hahn--Banach theorem for functionals on abstract convex cones
Eurasian mathematical journal, Tome 7 (2016) no. 3, pp. 89-99.

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We prove an analogue of the Hahn–Banach theorem on the extension of a linear functional with a convex estimate for each abstract convex cone with the cancellation law. Also we consider the special class of the so-called strict convex normed cones $(SCNC)$. For such structures we obtain an appropriate analogue of the Hahn–Banach separation theorem. On the base of this result we prove that each $(SCNC)$ is sublinearly, injectively and isometrically embedded in some Banach space. 
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F. S. Stonyakin. An analogue of the Hahn--Banach theorem for functionals on abstract convex cones. Eurasian mathematical journal, Tome 7 (2016) no. 3, pp. 89-99. http://geodesic.mathdoc.fr/item/EMJ_2016_7_3_a7/

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