Abstract
In this chapter we define the notion of a completely continuous operator from a Banach space to another Banach space and we present some simple properties of the completely continuous operators. Next we prove Brouwer’s fixed point theorem. Finally, we prove the famous Schauder fixed point theorem which, like Banach’s contraction principle, represents a fundamental result in nonlinear analysis.
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© 2002 Springer Science+Business Media Dordrecht
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Precup, R. (2002). Completely Continuous Operators on Banach Spaces. In: Methods in Nonlinear Integral Equations. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9986-3_3
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DOI: https://doi.org/10.1007/978-94-015-9986-3_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6114-0
Online ISBN: 978-94-015-9986-3
eBook Packages: Springer Book Archive