Opuscula Math. 30, no. 1 (2010), 69-77

Opuscula Mathematica

On some properties of the superposition operator on topological manifolds

Janusz Dronka

Abstract. 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.

Keywords: superposition operator, continuous function, topological manifold, Hammerstein integral equation.

Mathematics Subject Classification: 47H30, 45G15.

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  • Janusz Dronka
  • Technical University of Rzeszów, Department of Mathematics, ul. W. Pola 2, 35-959 Rzeszów, Poland
  • Received: 2009-08-18.
  • Revised: 2009-10-17.
  • Accepted: 2010-10-23.
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Cite this article as:
Janusz Dronka, On some properties of the superposition operator on topological manifolds, Opuscula Math. 30, no. 1 (2010), 69-77, http://dx.doi.org/10.7494/OpMath.2010.30.1.69

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