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. 
@article{EMJ_2016_7_3_a7,
     author = {F. S. Stonyakin},
     title = {An analogue of the {Hahn--Banach} theorem for functionals on abstract convex cones},
     journal = {Eurasian mathematical journal},
     pages = {89--99},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2016_7_3_a7/}
}
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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/