6533b82ffe1ef96bd129527c
RESEARCH PRODUCT
On dependence of sets of functions on the mean value of their elements
Uldis Raitumssubject
Convex hullDiscrete mathematicsSequenceBounded setMean valuemultivalued mappingsubsets of functions with fixed mean valueModeling and Simulationcontinuous dependenceQA1-939Element (category theory)Finite setAnalysisMathematicsMathematicsdescription
The paper considers, for a given closed bounded set M ⊂ R m and K = (0,1) n ⊂ R n , the set M = {h ϵ L2 (K;R m ) | h(x) ϵ M a.e.x ϵ K} and its subsets It is shown that, if a sequence {hk } ⊂ coM converges to an element hk ϵ M(hk ) there is h‘k ϵ M(ho ) such that h'k - hk → 0 as k → ∞ . If, in addition, the set M is finite or M is the convex hull of a finite set of elements, then the multivalued mapping h → M(h) is lower semicontinuous on coM. First published online: 14 Oct 2010
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-03-31 | Mathematical Modelling and Analysis |