On subdifferentials of convex functions. (English) Zbl 0928.49017

Kolomý, J.

Acta Univ. Carol., Math. Phys. 34, No. 2, 67-70 (1993).

The paper deals with subdifferentials of continuous convex functions \(f\) defined on a normed space \(X\). Conditions are given ensuring that subgradients of \(f\) belong to the complementary space of a closed subspace \(E\subseteq X\). Furthermore, the continuity and related properties of the duality mappings \(J: X\to 2^{X^*}\) and \(J: X^*\to 2^{X^{**}}\) of a Banach space \(X\) and its dual space \(X^*\) are investigated.

Reviewer: Hans-Peter Scheffler (MR 95d:49030)

MSC:

49J52	Nonsmooth analysis
46N10	Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
47N10	Applications of operator theory in optimization, convex analysis, mathematical programming, economics
58C20	Differentiation theory (Gateaux, Fréchet, etc.) on manifolds

Keywords:

subdifferentials; convex functions; normed space; dual space