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On d.c. mappings and differences of convex operators. (English) Zbl 1129.46311

Summary: Let \(C\) be an open convex set in a (real) normed linear space \(X\). A real-valued function \(f\) on \(C\) is d.c. if it can be represented as the difference of two continuous convex functions on \(C\). In this article, we study relationships between two possible generalizations of the notion of a d.c. function to mappings between normed spaces: “d.c. mapping” and “order d.c. mappings”.

MSC:

46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
49J53 Set-valued and variational analysis
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