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Convexity versus linearity. (English) Zbl 0928.49018

Rusev, P. (ed.) et al., Transform methods and special functions. Proceedings of the 1st international workshop, Bankya, Bulgaria, August 12–17, 1994. Sofia: SCT Publishing, 253-263 (1995).
Sections 1 and 2 present a racy introduction to some of the ideas of axiomatic convexity theory. Section 3 is concerned with generalizations of Mazur’s theorem on generic differentiability of convex functions and in particular with conditions which ensure that for a non-empty set-valued mapping \(\Gamma\) of a metric space \(X\) into a linear family \(\Phi\) of Lipschitz functions there exists a set \(A\) of first category such that \(\Gamma\) is single-valued and continuous on \(X\setminus A\).
This work is a continuation of [S. Rolewicz, Arch. Mat. 63, No. 6, 535-540 (1994; Zbl 0813.49018)].
For the entire collection see [Zbl 0914.00064].

MSC:

49J52 Nonsmooth analysis
49J53 Set-valued and variational analysis
46G05 Derivatives of functions in infinite-dimensional spaces

Citations:

Zbl 0813.49018
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