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Continuity of the Superposition of Set–Valued Functions
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N. Merentes
Published/Copyright:
June 4, 2010
Abstract
Let T, X, Y be topological spaces and F : T × X ↦ n(Y) be a set–valued function. We consider the Nemytskii operator generated by F which associates with every set–valued function G : T ↦ n(X) the superposition F(·,G(·)) : T ↦ n(Y). Conditions under which this superposition is lower or upper semicontinuous are presented.
Key words and phrases.: Superposition operator; set–valued functions; continuity; mid-convex functions
Received: 1996-05-15
Revised: 1996-11-11
Published Online: 2010-06-04
Published in Print: 1997-June
©Heldermann Verlag
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- Forced Oscillations of First Order Nonlinear Neutral Differential Equations
- Continuity of the Superposition of Set–Valued Functions
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- Optimality Conditions for Control Problems Governed by Abstract Semilinear Differential Equations in Complex Banach Spaces
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Keywords for this article
Superposition operator;
set–valued functions;
continuity;
mid-convex functions
Articles in the same Issue
- Optimal Synthesis for Nonoscillatory Controlled Objects
- Forced Oscillations of First Order Nonlinear Neutral Differential Equations
- Continuity of the Superposition of Set–Valued Functions
- On the Uniqueness of Lebesgue and Borel Measures
- Optimality Conditions for Control Problems Governed by Abstract Semilinear Differential Equations in Complex Banach Spaces
- On the Continuity of Random Operators
- Norms on Possibilities II: More CCC Ideals on 2ω
- Stationary Solutions for Heat Equation Perturbed by General Additive Noise
- Note on Decreasing Rearrangement of Fourier Series
