Journal of Applied Analysis Vol. 3, No. 1, pp. 4348 (2003) 

Continuity of the superposition of setvalued functionsN. Merentes, K. Nikodem and S. RivasNelson MerentesCentral University of Venezuela Caracas Venezuela Kazimierz Nikodem Katedra Matematyki Filia Politechniki Lodzkiej BielskoBiala, 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 setvalued function. We consider the Nemytskii operator generated by $F$ which associates with every setvalued 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, setvalued functions, continuity, midconvex functions Classification (MSC2000): 47H99, 54C60, 26B25 Full text of the article:
Electronic version published on: 12 Jun 2003. This page was last modified: 12 Jun 2003.
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