Minimal pairs representing selections of four linear functions in .
-minimal pairs of compact convex sets.
Decomposition of set functions with values in a topological semigroups
Weak compactness of the range of a set-valued measure
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Minimal pairs of bounded closed convex sets
The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.
On the number of minimal pairs of compact convex sets that are not translates of one another
Let [A,B] be the family of pairs of compact convex sets equivalent to (A,B). We prove that the cardinality of the set of minimal pairs in [A,B] that are not translates of one another is either 1 or greater than ℵ₀.
Total variation of a set-valued measure
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Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule
On the reduction of pairs of bounded closed convex sets
Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The second theorem...
General methods of constructing equivalent minimal pairs not unique up to translation.
In this paper we give general methods of construction of various equivalent minimal pairs of compact convex sets that are not translates of one another.
Some extensions of the Riesz-Thorin theorem to generalized Orlicz spaces
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A totally non-atomic set-valued measures
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Linear operators in modular spaces
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