Displaying similar documents to “Approximation of Univariate Set-Valued Functions - an Overview”

Approximation of set-valued functions with compact images-an overview

Nira Dyn, Elza Farkhi (2006)

Banach Center Publications


Continuous set-valued functions with convex images can be approximated by known positive operators of approximation, such as the Bernstein polynomial operators and the Schoenberg spline operators, with the usual sum between numbers replaced by the Minkowski sum of sets. Yet these operators fail to approximate set-valued functions with general sets as images. The Bernstein operators with growing degree, and the Schoenberg operators, when represented as spline subdivision schemes, converge...

Compact operators and approximation spaces

Fernando Cobos, Oscar Domínguez, Antón Martínez (2014)

Colloquium Mathematicae


We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.

Continuous dependence on parameters of the fixed points set for some set-valued operators

Eduard Kirr, Adrian Petruel (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization


In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.

On the norm of a projection onto the space of compact operators

Joosep Lippus, Eve Oja (2007)

Studia Mathematica


Let X and Y be Banach spaces and let 𝓐(X,Y) be a closed subspace of 𝓛(X,Y), the Banach space of bounded linear operators from X to Y, containing the subspace 𝒦(X,Y) of compact operators. We prove that if Y has the metric compact approximation property and a certain geometric property M*(a,B,c), where a,c ≥ 0 and B is a compact set of scalars (Kalton's property (M*) = M*(1, {-1}, 1)), and if 𝓐(X,Y) ≠ 𝒦(X,Y), then there is no projection from 𝓐(X,Y) onto 𝒦(X,Y) with norm less than...

On a class of Szász-Mirakyan type operators

Zbigniew Walczak (2008)

Czechoslovak Mathematical Journal


The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.