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On a separation theorem for delta-convex functions. (English) Zbl 1464.26011

Necessary and sufficient conditions for guaranteeing that two functions can be separated with respect to the Lorentz partial ordering by a d.c (difference of convex functions), here called delta-convex functions, are studied. As an application a stability problem for delta-convexity is investigated.

MSC:

26B25 Convexity of real functions of several variables, generalizations
26A51 Convexity of real functions in one variable, generalizations
39B22 Functional equations for real functions
39B62 Functional inequalities, including subadditivity, convexity, etc.
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