On some properties of the superposition operator on topological manifolds

On some properties of the superposition operator on topological manifolds

In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein int...

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Bibliographic Details
Main Author: Janusz Dronka
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2010-01-01
Series:Opuscula Mathematica
Subjects:
superposition operator
continuous function
topological manifold
Hammerstein integral equation
Online Access:http://www.opuscula.agh.edu.pl/vol30/1/art/opuscula_math_3005.pdf
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spelling doaj-1885e58b38844580ab44122d3fbd5a0e2020-11-24T20:51:33ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742010-01-013016977http://dx.doi.org/10.7494/OpMath.2010.30.1.693005On some properties of the superposition operator on topological manifoldsJanusz Dronka0Technical University of Rzeszów, Department of Mathematics, ul. W. Pola 2, 35-959 Rzeszów, PolandIn this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.http://www.opuscula.agh.edu.pl/vol30/1/art/opuscula_math_3005.pdfsuperposition operatorcontinuous functiontopological manifoldHammerstein integral equation
collection DOAJ
language English
format Article
sources DOAJ
author Janusz Dronka
spellingShingle Janusz Dronka
On some properties of the superposition operator on topological manifolds
Opuscula Mathematica
superposition operator
continuous function
topological manifold
Hammerstein integral equation
author_facet Janusz Dronka
author_sort Janusz Dronka
title On some properties of the superposition operator on topological manifolds
title_short On some properties of the superposition operator on topological manifolds
title_full On some properties of the superposition operator on topological manifolds
title_fullStr On some properties of the superposition operator on topological manifolds
title_full_unstemmed On some properties of the superposition operator on topological manifolds
title_sort on some properties of the superposition operator on topological manifolds
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2010-01-01
description In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
topic superposition operator
continuous function
topological manifold
Hammerstein integral equation
url http://www.opuscula.agh.edu.pl/vol30/1/art/opuscula_math_3005.pdf
work_keys_str_mv AT januszdronka onsomepropertiesofthesuperpositionoperatorontopologicalmanifolds
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