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On the Best Approximation of Set-Valued Functions
1997Let M be a Hausdorff compact topological space, let C(M) be the Banach space of the continuous on M functions supplied with the supremum norm and let V C C(M) be a finite dimensional subspace of C(M). The problem of the Chebyshev approximation of a function f ∈ C(M) by functions from V can be put in the form \({{\max }_{{t \in M}}}\max \left\{ {f\left(
IVANOV, IVAN GINCHEV, ARMIN HOFFMANN
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Integrals of Set-Valued Functions with a Countable Range
Mathematics of Operations Research, 1996Approximate versions, both of Lyapunov-type results on the compactness and convexity of the integral of a correspondence, and Fatou-type results on the preservation of upper semicontinuity by integration, are well known in the context of an infinite dimensional space. We report exact versions of these two types of results for integrals of Banach space
M. Ali Khan, Yeneng Sun
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On Nemytskii operator for set-valued functions
Publicationes Mathematicae Debrecen, 1999The author presents generalizations (in some sense) of her previous results that appeared in [Publ. Math. 54, No. 1-2, 33-37 (1999; Zbl 0921.47056)]. In fact, here she treats the problem of characterizing those vector-valued, or set-valued functions that generate such a Nemytskij operator which maps a \(\text{lip}^2\) space (space of functions with ...
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Semigroups of set-valued functions
Publicationes Mathematicae Debrecen, 1997Summary: It is proved that a measurable semigroup of linear continuous set-valued functions satisfying some additional assumptions is majorized by a one-parameter family of an exponential type generated by it.
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STABILITY AND SET-VALUED FUNCTIONS
1998Some interesting connections between the stability results of Chapter 1 as well as the theory of subadditive set-valued functions has been pointed out by several authors. We begin with a work by W. Smajdor (1986) which generalizes for set-valued functions some well-known theorems on linearity for ordinary functions, starting with an example (see also ...
Donald H. Hyers +2 more
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On a family of set-valued functions
Publicationes Mathematicae Debrecen, 1995It is proved that if \(C\) is a closed convex cone in a Banach space and \(G:C\to cc(C)\) is a continuous linear set-valued function, then for every \(x\in C\) and \(t\geq 0\) the series \[ B^t(x)= \sum^\infty_{i=0} {t^i\over i!} G^i(x) \] is convergent. Moreover, the set-valued functions \(B^t\) are linear, continuous on \(\text{int C}\) and it holds \
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On interval-valued pre-(quasi-)overlap functions
Information Sciences, 2022Yuntian Wang, Bao Qing Hu
exaly
General interval-valued overlap functions and interval-valued overlap indices
Information Sciences, 2020Tiago Da Cruz Asmus +2 more
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On the classification of set-valued functions
1984This interesting paper presents some general theorems on multifunctions. One result strengthens a selection theorem of \textit{K. Kuratowski} and \textit{C. Ryll-Nardzewski} [Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 13, 397-403 (1965)], a second contains two selection theorems of \textit{E. Michael} [Ann. Math., II. Ser.
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