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Set-valued mapping monotonicity as characterization of D.C functions. (English) Zbl 1222.46005
Summary: Using a result of K.-C. Chang [J. Math. Anal. Appl. 80, 102–129 (1981; Zbl 0487.49027)], we give a characterization of locally Lipschitz functions which are differences of convex functions defined on a Banach space (not necessarily Asplund) in terms on maximal cyclically monotone set-valued mappings. A subdifferential integration of locally D.C functions is also given.

46A40 Ordered topological linear spaces, vector lattices
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46B40 Ordered normed spaces
46B42 Banach lattices
Full Text: DOI
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