Abstract
The quasidifferential calculus, separation of convex sets and the Demyanov difference
Highlights
The quasidifferential calculus which was developed by V
Rubinov around 1980 looks at the first glance as an exact subdifferential calculus for pairs of subdifferentials which satisfies the classical rules of additivity and the Leibniz rules
A closer view shows that the quasidifferential calculus had far-reaching consequences on generalized convexity which did lead to a fun
Summary
The quasidifferential calculus which was developed by V. There exists an obvious similarity between quasidifferentiation and the Frechet differential calculus in finite dimensional spaces, by extending the notion of a derivative from a linear functional to a difference of sublinear functions. This property, transformed to the quasidifferential calculus, would request the existence of a norm for the space DCH(X), under which it becomes a Banach space This can be satisfied as the following result shows, which reflects a further important analogy between the Frechet and the quasidifferential calculus. The triangle inequality follows from the arbitrariness of ε > 0 In this way we have proved that DCH(X) is a normed vector space. Let (φn)n∈N be a sequence of elements of DCH(X) such that 1 φn Δ < 2n
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