On preponderant maxima
Small non-σ-porous sets in topologically complete metric spaces
On cluster sets of arbitrary functions
Delta-convex mappings between Banach spaces and applications
We investigate delta-convex mappings between normed linear spaces. They provide a generalization of functions which are representable as a difference of two convex functions (labelled as 5-convex or d.c. functions) and are considered in many articles. We show that delta-convex mappings have many good differentiability properties of convex functions and the class of them is very stable. For example, the class of locally delta-convex mappings is closed under superpositions and (in some situations)...
On the differentiation of convex functions
On the points of multivaluedness of monotone operators
On the singlevaluedness and differentiation of metric projections
On metric projections and distance functions in Banach spaces
A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
On the Fréchet differentiability of distance functions
On Residuality of the Set of Rotund Norms on a Banach Space.
On -porous sets in abstract spaces.
Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.
Stronger estimates of smallness of sets of Frechet nondifferentiability of convex functions
Typical measurable function in the topology of close approximation.
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