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The completion of the space of convex, bounded sets with respect to the Demyanov metric

Grzybowski J., Leśniewski A., Rzeżuchowski T.

Demonstratio Mathematica

2013

Vol. 46, nr 1

191--196

The Demyanov metric in the family of convex, compact sets in finite dimensional spaces has been recently extended to the family of convex, bounded sets – not necessarily closed. In this note it is shown that these spaces are not complete and a model for the completion is proposed. A full answer is given in R2 and the situation in higher dimensions is discussed.

The Demyanov metric and measurable multifunctions

Leśniewski A.

Journal of Mathematics and Applications

2010

Vol. 33

61-65

We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.

Some results for the reflection problems in Hilbert spaces

Barbu V., Da Prato G.

Control and Cybernetics

2008

Vol. 37, no 4

797-810

This work is concerned with existence and uniqueness of a solution of a stochastic variational inequality on closed convex bounded subsets with nonempty interior and smooth boundary of a Hilbert space H (the reflection problem).

Rough Equalities From Posets and Rough Difference Orders

Mani A.

Fundamenta Informaticae

2002

Vol. 53, nr 3,4

321-333

In the initial section of this research paper rough equalities from partially ordered approximation spaces are investigated. Special types of rough equalities are characterized via convex and other types of sets. Extension of these to all types of rough equalities is also indicated. Two new theories of `Rough Difference Orders' which are often more general and distinct from that of `Rough Orders' are also developed in the last section by the present author.