Journal of Applied Analysis EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 3, No. 1, pp. 43-48 (2003)

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Continuity of the superposition of set-valued functions

N. Merentes, K. Nikodem and S. Rivas

Nelson Merentes
Central University
of Venezuela Caracas
Venezuela
Kazimierz Nikodem
Katedra Matematyki
Filia Politechniki Lodzkiej
Bielsko-Biala, Poland
Sergio Rivas
Open National University
Caracas, Venezuela

Abstract: Let $T$, $X$, $Y$ be topological spaces and $F:\; T \times X \mapsto n(Y)$ be a set-valued function. We consider the Nemytskii operator generated by $F$ which associates with every set-valued function $G:\; T \mapsto n(X)$ the superposition $F(\cdot, G(\cdot)):\; T \mapsto n(Y)$. Conditions under which this superposition is lower or upper semicontinuous are presented.

Keywords: Superposition operator, set-valued functions, continuity, midconvex functions

Classification (MSC2000): 47H99, 54C60, 26B25

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Electronic version published on: 12 Jun 2003. This page was last modified: 12 Jun 2003.

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© 2003 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition