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On the reduction of pairs of bounded closed convex sets

100%

Grzybowski J., Pallaschke D., Urbański R.

Studia Mathematica

2008

tom 189

nr 1

1-12

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 generalizes and unifies two main techniques of reduction of pairs of compact convex sets.

Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule

87%

Grzybowski J., Pallaschke D., Urbański R.

Control and Cybernetics

2007

tom 36

nr 4

911-924

Ograniczanie wyników

1 Control and Cybernetics

1 Studia Mathematica

2 Grzybowski J.

2 Pallaschke D.

2 Urbański R.

1 2008

1 2007

Wyniki wyszukiwania

On the reduction of pairs of bounded closed convex sets

Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule