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Monotonically upper semicontinuity
Bulletin of the Kyushu Institute of Technology. Pure and applied mathematics, 2005Summary: We show that a function \(f\) from a topological vector space \(E\) into \(\mathbb{R}\) is uniformly continuous if and only if \(f\) is monotonically upper semicontinuous, a notion introduced by Y. Kimua, K. Tanaka and T. Tanaka. We also discuss similar conditions for monotonically upper semicontinuity.
Suzuki, Tomonari +2 more
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Approximation of Mappings with Values Which Are Upper Semicontinuous Functions [PDF]
Journal of Approximation Theory, 2001 In this paper we study some aspects of the approximation of mappings taking values in a special class of upper semicontinuous functions. Some Korovkin type theorems for positive linear operators are obtained, and consequences of these theorems for a ...
Pedro Teran, MIGUEL López-Dı́Az
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Mathematical Notes of the Academy of Sciences of the USSR, 1977
It is proved that the following conditions are equivalent: the function ϕ [a, b]→R is absolutely upper semicontinuous (see [1]); ϕ is a function of bounded variation with decreasing singular part; there exists a summable function g: [a, b] → R such that for anyt′∈[a, b] andt″∈[t′, b], we have ϕ(t″)−ϕ(t′)⩽∫ t′ t″ g (s) ds.
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It is proved that the following conditions are equivalent: the function ϕ [a, b]→R is absolutely upper semicontinuous (see [1]); ϕ is a function of bounded variation with decreasing singular part; there exists a summable function g: [a, b] → R such that for anyt′∈[a, b] andt″∈[t′, b], we have ϕ(t″)−ϕ(t′)⩽∫ t′ t″ g (s) ds.
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A Note on Random Upper Semicontinuous Functions
2007This note aims at presenting the most general framework for a class U of random upper semicontinuous functions, namely random elements whose sample paths are upper semicontinuous (u.s.c.) functions, defined on some locally compact, Hausdorff and second countable base space, extending Matheron’s framework for random closed sets.
Hung T. Nguyen 0002 +3 more
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Upper Semicontinuous Decompositions of E 3
The Annals of Mathematics, 1957In this paper it is shown that monotone upper semicontinuous decompositions of E3 satisfying certain additional conditions have decomposition spaces which are topologically equivalent to E3. When these results were first obtained several years ago, we had some misgivings about imposing certain of these conditions since it was not known at that time ...
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Upper semicontinuity of Nemytskij operators
Annali di Matematica Pura ed Applicata, 1991The authors give a growth condition on a multivalued nonlinear function \(G=G(\lambda,u)\), under which the upper semicontinuity of the function \(G(\lambda,\cdot)\) implies the upper semicontinuity of the multivalued Nemytskij operator generated by \(G\) between two Lebesgue-Bochner spaces. Similar results have been given by the reviewer, \textit{H. T.
CELLINA, ARRIGO +2 more
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A Chain Rule for Upper Semicontinuous (CF)-Mappings
Journal of Global Optimization, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Upper semicontinuity of joint spectra
2022This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
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Upper semicontinuity of parametric projections
Set-Valued Analysis, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Upper semicontinuity of closed-convex-valued multifunctions
Mathematical Methods of Operations Research, 2003The authors study the (Berge) upper semicontinuity of a generic multifunction assigning to each parameter in a metric space a closed convex subset in Euclidean \(n\)-space. An example is the feasible set mapping associated with a parametric family of convex semi-infinite programming problems.
María J. Cánovas +3 more
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