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On dependence of sets of functions on the mean value of their elements

    Uldis Raitums Affiliation

Abstract

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

Keyword : multivalued mapping, subsets of functions with fixed mean value, continuous dependence

How to Cite
Raitums, U. (2009). On dependence of sets of functions on the mean value of their elements. Mathematical Modelling and Analysis, 14(1), 91-98. https://doi.org/10.3846/1392-6292.2009.14.91-98
Published in Issue
Mar 31, 2009
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